ConceptID,ConceptLabel,Dependencies,TaxonomyID
1,Function,,FOUND
2,Domain and Range,1,FOUND
3,Function Notation,1,FOUND
4,Composite Function,1|3,FOUND
5,Inverse Function,1|2,FOUND
6,Graphing Functions,1|2,FOUND
7,Piecewise Function,1|6,FOUND
8,Even and Odd Functions,1|6,FOUND
9,Function Transformations,1|6,FOUND
10,Polynomial Function,1|3,FOUND
11,Rational Function,10,FOUND
12,Exponential Function,1|3,FOUND
13,Logarithmic Function,12,FOUND
14,Trigonometric Function,1,FOUND
15,Unit Circle,14,FOUND
16,Radian Measure,15,FOUND
17,Trigonometric Identities,14|15,FOUND
18,Coordinate System,,FOUND
19,Number Line,18,FOUND
20,Real Numbers,19,FOUND
21,Limit,1|20,LIMIT
22,Limit Notation,21,LIMIT
23,Intuitive Limit,21,LIMIT
24,One-Sided Limit,21|22,LIMIT
25,Left-Hand Limit,24,LIMIT
26,Right-Hand Limit,24,LIMIT
27,Two-Sided Limit,25|26,LIMIT
28,Limit Existence,27,LIMIT
29,Limit Laws,21|28,LIMIT
30,Sum Rule for Limits,29,LIMIT
31,Product Rule for Limits,29,LIMIT
32,Quotient Rule for Limits,29,LIMIT
33,Constant Multiple Rule,29,LIMIT
34,Power Rule for Limits,29,LIMIT
35,Direct Substitution,29|10,LIMIT
36,Indeterminate Form,35,LIMIT
37,Zero Over Zero Form,36,LIMIT
38,Infinity Over Infinity,36,LIMIT
39,Algebraic Limit Technique,36|37,LIMIT
40,Factoring for Limits,39,LIMIT
41,Rationalization,39,LIMIT
42,Complex Fractions,39,LIMIT
43,Squeeze Theorem,29,LIMIT
44,Special Trig Limits,43|14,LIMIT
45,Sin x Over x Limit,44,LIMIT
46,Limit of Composition,4|29,LIMIT
47,Limits from Graphs,6|23,LIMIT
48,Limits from Tables,23,LIMIT
49,Numerical Estimation,48,LIMIT
50,Infinite Limit,21,LIMIT
51,Continuity,21|28,CONT
52,Continuity at a Point,51,CONT
53,Three Conditions,52,CONT
54,Continuity on Interval,52,CONT
55,One-Sided Continuity,52|24,CONT
56,Continuous Function,54,CONT
57,Discontinuity,51,CONT
58,Removable Discontinuity,57|37,CONT
59,Jump Discontinuity,57|24,CONT
60,Infinite Discontinuity,57|50,CONT
61,Essential Discontinuity,57,CONT
62,Continuous Extension,58,CONT
63,Removing Discontinuities,58|62,CONT
64,Piecewise Continuity,7|52,CONT
65,Continuity of Composites,4|56,CONT
66,Continuity of Polynomials,10|56,CONT
67,Continuity of Rationals,11|56|57,CONT
68,Continuity of Trig,14|56,CONT
69,Continuity of Exp Log,12|13|56,CONT
70,Intermediate Value Thm,54|56,CONT
71,Asymptote,50|57,ASYM
72,Vertical Asymptote,71|60,ASYM
73,Horizontal Asymptote,71,ASYM
74,Oblique Asymptote,73|11,ASYM
75,Limit at Infinity,21|73,ASYM
76,End Behavior,75,ASYM
77,Behavior Near Asymptote,72|75,ASYM
78,One-Sided Infinite Limit,50|24,ASYM
79,Comparing Growth Rates,75|12,ASYM
80,Dominant Term,79|10,ASYM
81,Rational End Behavior,11|76,ASYM
82,Exponential Growth Rate,12|79,ASYM
83,Logarithmic Growth Rate,13|79,ASYM
84,Polynomial Growth Rate,10|79,ASYM
85,Rate of Change,1,DERIV
86,Average Rate of Change,85,DERIV
87,Instantaneous Rate,86|21,DERIV
88,Difference Quotient,86,DERIV
89,Secant Line,88|6,DERIV
90,Tangent Line,89|21,DERIV
91,Slope of Tangent,90,DERIV
92,Derivative Definition,91|87,DERIV
93,Limit Definition Deriv,92|21,DERIV
94,Derivative at a Point,93,DERIV
95,Derivative Function,94,DERIV
96,Derivative Notation,95,DERIV
97,Prime Notation,96,DERIV
98,Leibniz Notation,96,DERIV
99,Differentiable Function,95,DERIV
100,Differentiability,99,DERIV
101,Differentiability Point,100|94,DERIV
102,One-Sided Derivative,101|24,DERIV
103,Non-Differentiable Pts,100,DERIV
104,Corner Point,103,DERIV
105,Cusp,103,DERIV
106,Vertical Tangent Point,103|90,DERIV
107,Derivative from Graph,95|6,DERIV
108,Derivative from Table,95|48,DERIV
109,Symmetric Difference,88,DERIV
110,Diff Implies Continuous,100|56,DERIV
111,Continuous Not Implies,110|103,DERIV
112,Local Linearity,90|99,DERIV
113,Tangent Approximation,112,DERIV
114,Instantaneous Velocity,87|92,DERIV
115,Derivative Rules,95,DRULE
116,Constant Rule,115,DRULE
117,Power Rule Derivative,115,DRULE
118,Sum Rule Derivative,115,DRULE
119,Difference Rule Deriv,115,DRULE
120,Constant Multiple Deriv,115,DRULE
121,Linear Combination,118|120,DRULE
122,Polynomial Derivative,117|121,DRULE
123,Derivative of x to n,117,DRULE
124,Negative Exponent Deriv,123,DRULE
125,Fractional Exponent,123,DRULE
126,Derivative of Root,125,DRULE
127,Product Rule,115,DRULE
128,Product Rule Formula,127,DRULE
129,Quotient Rule,127,DRULE
130,Quotient Rule Formula,129,DRULE
131,Reciprocal Rule,129,DRULE
132,Derivative of Sine,115|14,DRULE
133,Derivative of Cosine,132,DRULE
134,Derivative of Tangent,132|133|129,DRULE
135,Derivative of Cotangent,134,DRULE
136,Derivative of Secant,132|133|129,DRULE
137,Derivative of Cosecant,136,DRULE
138,Derivative of e to x,115|12,DRULE
139,Derivative of a to x,138,DRULE
140,Derivative of ln x,115|13,DRULE
141,Derivative of log x,140,DRULE
142,Combining Rules,121|127|129,DRULE
143,Simplifying First,142,DRULE
144,Chain Rule,4|95,CHAIN
145,Chain Rule Formula,144,CHAIN
146,Composition Derivative,144,CHAIN
147,Inside Function,145,CHAIN
148,Outside Function,145,CHAIN
149,Nested Chain Rule,145,CHAIN
150,Leibniz Chain Rule,145|98,CHAIN
151,Derivative of f of g,146,CHAIN
152,Recognizing Composition,147|148,CHAIN
153,Power Chain Rule,145|117,CHAIN
154,Trig Chain Rule,145|132,CHAIN
155,Exponential Chain Rule,145|138,CHAIN
156,Log Chain Rule,145|140,CHAIN
157,Multiple Chain Rule,149,CHAIN
158,General Power Rule,153,CHAIN
159,Combining Chain Rule,145|142,CHAIN
160,Implicit Function,1,IMPL
161,Implicit Equation,160,IMPL
162,Implicit Differentiation,161|144,IMPL
163,dy dx Implicitly,162,IMPL
164,Treating y as Function,162,IMPL
165,Implicit Chain Rule,162|144,IMPL
166,Solving for dy dx,163,IMPL
167,Second Deriv Implicit,166,IMPL
168,Tangent Line Implicit,166|90,IMPL
169,Inverse Function Thm,5|95,IMPL
170,Derivative of Inverse,169,IMPL
171,Inverse Deriv Formula,170,IMPL
172,Graphical Inverse Deriv,170|6,IMPL
173,Derivative of Arcsin,170|14,IMPL
174,Derivative of Arccos,173,IMPL
175,Derivative of Arctan,173,IMPL
176,Derivative of Arcsec,175,IMPL
177,Derivative of Arccsc,176,IMPL
178,Derivative of Arccot,175,IMPL
179,Inverse Trig Domain,173,IMPL
180,Logarithmic Differentiate,140|162,IMPL
181,Differentiating Products,180,IMPL
182,Differentiating Powers,180,IMPL
183,Variable Exponents,182,IMPL
184,Higher-Order Derivative,95,HIGH
185,Second Derivative,184,HIGH
186,Third Derivative,185,HIGH
187,nth Derivative,186,HIGH
188,Second Deriv Notation,185,HIGH
189,f Double Prime,188,HIGH
190,d2y dx2 Notation,188,HIGH
191,Velocity from Position,114|185,HIGH
192,Acceleration,191,HIGH
193,Jerk,192|186,HIGH
194,Position Velocity Accel,191|192,HIGH
195,Speed vs Velocity,191,HIGH
196,Direction of Motion,195,HIGH
197,Speeding Up Slowing,192|196,HIGH
198,Higher Trig Derivatives,187|132,HIGH
199,Related Rates,162|87,APPL
200,Related Rates Setup,199,APPL
201,Implicit in Context,199|162,APPL
202,Rate Variables,200,APPL
203,Related Rates Diagram,200,APPL
204,Ladder Problem,199|203,APPL
205,Balloon Problem,199|203,APPL
206,Shadow Problem,199|203,APPL
207,Conical Tank Problem,199|203,APPL
208,Distance Rate Problem,199|203,APPL
209,Linear Approximation,112|113,APPL
210,Tangent Line Approx,209,APPL
211,Linearization Formula,209,APPL
212,Error in Approximation,209,APPL
213,Differential,98|209,APPL
214,dy Notation,213,APPL
215,dx Notation,213,APPL
216,Differential Approx,213|212,APPL
217,Marginal Analysis,95|87,APPL
218,Marginal Cost,217,APPL
219,Marginal Revenue,217,APPL
220,Marginal Profit,218|219,APPL
221,Economics Interpretation,217,APPL
222,Units of Derivative,95|87,APPL
223,Rate Interpretation,222,APPL
224,Derivative in Context,223,APPL
225,Population Rate,224,APPL
226,Temperature Rate,224,APPL
227,Concentration Rate,224,APPL
228,L'Hospital's Rule,36|37|38,APPL
229,L'Hospital Conditions,228,APPL
230,Zero Over Zero Apply,228|37,APPL
231,Inf Over Inf Apply,228|38,APPL
232,Indeterminate Products,228,APPL
233,Zero Times Infinity,232,APPL
234,Indeterminate Powers,228,APPL
235,One to Infinity,234,APPL
236,Repeated L'Hospital,228,APPL
237,Verify L'Hospital,229,APPL
238,Mean Value Theorem,56|99,ANAL
239,MVT Statement,238,ANAL
240,MVT Conditions,238,ANAL
241,MVT Conclusion,239,ANAL
242,Rolle's Theorem,238,ANAL
243,Rolle's Conditions,242,ANAL
244,MVT Applications,241,ANAL
245,Average vs Instant MVT,244|86|87,ANAL
246,Extreme Value Theorem,56|54,ANAL
247,EVT Statement,246,ANAL
248,EVT Conditions,246,ANAL
249,Global Maximum,246,ANAL
250,Global Minimum,246,ANAL
251,Local Maximum,95,ANAL
252,Local Minimum,95,ANAL
253,Critical Point,95|251|252,ANAL
254,Critical Number,253,ANAL
255,Where f Prime Zero,254,ANAL
256,Where f Prime DNE,254|103,ANAL
257,First Derivative Test,253|255,ANAL
258,Sign Chart,257,ANAL
259,Increasing Function,257,ANAL
260,Decreasing Function,257,ANAL
261,Monotonicity,259|260,ANAL
262,Sign Change Analysis,258,ANAL
263,Second Derivative Test,185|253,ANAL
264,Concavity,185,ANAL
265,Concave Up,264,ANAL
266,Concave Down,264,ANAL
267,Inflection Point,264|265|266,ANAL
268,Point of Inflection,267,ANAL
269,Candidates Test,249|250|254,ANAL
270,Closed Interval Method,269,ANAL
271,Endpoint Extrema,270,ANAL
272,Curve Sketching,257|264,CURV
273,Complete Curve Analysis,272,CURV
274,f f Prime f Dbl Prime,272|185,CURV
275,Graph from Derivative,274,CURV
276,Derivative from Graph,275,CURV
277,Connecting Three Graphs,274|275|276,CURV
278,Domain Analysis,2|272,CURV
279,Intercept Analysis,272,CURV
280,Symmetry Analysis,8|272,CURV
281,Asymptote Analysis,71|272,CURV
282,Increasing Decreasing,259|260|272,CURV
283,Local Extrema Analysis,257|272,CURV
284,Concavity Analysis,264|272,CURV
285,Inflection Analysis,267|272,CURV
286,Optimization,253|269,OPT
287,Optimization Problem,286,OPT
288,Objective Function,287,OPT
289,Constraint Equation,287,OPT
290,Primary Equation,288|289,OPT
291,Setting Up Optimization,290,OPT
292,Maximizing Area,291,OPT
293,Minimizing Distance,291,OPT
294,Minimizing Cost,291,OPT
295,Maximizing Volume,291,OPT
296,Fencing Problem,292,OPT
297,Box Problem,295,OPT
298,Can Problem,295,OPT
299,Closest Point Problem,293,OPT
300,Maximum Profit,294|220,OPT
301,Applied Optimization,287,OPT
302,Verifying Maximum,263|269,OPT
303,Verifying Minimum,263|269,OPT
304,Second Deriv Verify,302|303,OPT
305,Endpoint Consideration,271|287,OPT
306,Practical Domain,2|287,OPT
307,Antiderivative,95,INTEG
308,Indefinite Integral,307,INTEG
309,Integral Notation,308,INTEG
310,Integrand,309,INTEG
311,Variable of Integration,309,INTEG
312,Constant of Integration,308,INTEG
313,General Antiderivative,308|312,INTEG
314,Particular Antideriv,313,INTEG
315,Power Rule Integration,308|117,INTEG
316,Constant Rule Integr,308,INTEG
317,Sum Rule Integration,308,INTEG
318,Difference Rule Integr,308,INTEG
319,Constant Multiple Integ,308,INTEG
320,Basic Trig Integrals,308|132,INTEG
321,Integral of Sin x,320,INTEG
322,Integral of Cos x,320,INTEG
323,Integral of Sec Squared,320,INTEG
324,Integral of Csc Squared,320,INTEG
325,Integral of Sec Tan,320,INTEG
326,Integral of Csc Cot,320,INTEG
327,Integral of e to x,308|138,INTEG
328,Integral of a to x,327,INTEG
329,Integral of 1 Over x,308|140,INTEG
330,Natural Log Integral,329,INTEG
331,Inverse Trig Integrals,308|173,INTEG
332,Arcsin Integral,331,INTEG
333,Arctan Integral,331,INTEG
334,Arcsec Integral,331,INTEG
335,Riemann Sum,86|308,RIEM
336,Left Riemann Sum,335,RIEM
337,Right Riemann Sum,335,RIEM
338,Midpoint Riemann Sum,335,RIEM
339,Trapezoidal Rule,335,RIEM
340,Summation Notation,335,RIEM
341,Sigma Notation,340,RIEM
342,Index of Summation,341,RIEM
343,Limit of Riemann Sum,335|21,RIEM
344,Definite Integral,343,RIEM
345,Definite Integral Notat,344,RIEM
346,Limits of Integration,345,RIEM
347,Fundamental Theorem,344|307,FTC
348,FTC Part One,347,FTC
349,FTC Part Two,347,FTC
350,Evaluation Theorem,349,FTC
351,Accumulation Function,348,FTC
352,Integral as Function,351,FTC
353,Derivative of Integral,348,FTC
354,FTC Chain Rule,348|144,FTC
355,Net Change Theorem,349,FTC
356,Net Signed Area,344,FTC
357,Area Under Curve,356,FTC
358,Integral Properties,344,FTC
359,Additivity Property,358,FTC
360,Reversing Limits,358,FTC
361,Zero Width Integral,358,FTC
362,Integral of Sum,358,FTC
363,Integral Bounds Split,359,FTC
364,Comparison Property,358,FTC
365,Even Function Integral,8|358,FTC
366,Odd Function Integral,8|358,FTC
367,Average Value,344,FTC
368,Average Value Formula,367,FTC
369,Mean Value Integral,367|238,FTC
370,u-Substitution,308|144,TECH
371,Substitution Method,370,TECH
372,Choosing u,371,TECH
373,du Calculation,371,TECH
374,Back Substitution,371,TECH
375,Definite Substitution,370|344,TECH
376,Changing Bounds,375,TECH
377,Long Division Method,308|11,TECH
378,Completing Square,308,TECH
379,Partial Fractions,308|11,TECH
380,Integration Strategy,370|377|378,TECH