Upload app.py

app.py

@@ -1632,6 +1632,11 @@ def plot_graph(problem: str, sympy_info: dict):
         plt.tight_layout()
         st.pyplot(fig)
         plt.close(fig)  # free memory
+        # Caption below graph
+        deriv_label = "  🟠 f'(x)" if sympy_info.get("type") == "Derivative" else ""
+        st.caption(f"📊 $y = {sp.latex(expr_sym)}$ "
+                   f"| x ∈ [{x_min}, {x_max}]"
+                   f"{deriv_label}")
 
     except Exception:
         pass  # silent fallback — never crash the app
@@ -1741,8 +1746,17 @@ def ask_ai(problem: str, sympy_info: dict, history: list) -> str:
         "  ✅ **Final Answer:** $$\\boxed{answer}$$\n"
         "  → Never skip this structure. Never merge steps. Never jump to answer without showing work.\n"
         "  → If user says plot/draw/graph/sketch/visualize: a real graph renders automatically.\n"
-        "     Do NOT describe the graph in text. Do NOT draw ASCII art. Do NOT say you cannot draw.\n"
-        "     Just say: '📊 Here is the graph of $f(x) = ...$' and stop. Graph shows automatically.\n\n"
+        "     Do NOT draw ASCII art. Do NOT say you cannot draw.\n"
+        "     Give this SHORT response only — then graph renders below automatically:\n"
+        "       📌 **Function:** state f(x) clearly in LaTeX\n"
+        "       🔍 **Key Features:**\n"
+        "         - Domain and range\n"
+        "         - x-intercepts: solve f(x)=0\n"
+        "         - y-intercept: f(0)\n"
+        "         - Turning points / vertex if any\n"
+        "         - Behavior as $x \\to \\pm\\infty$\n"
+        "       📊 **Graph** is shown below.\n"
+        "     Keep it SHORT — max 8 lines. No long paragraphs. No step-by-step for graph requests.\n\n"
 
         "RULE 2 — LATEX (zero exceptions):\n"
         "  - Inline math (inside a sentence): $expression$\n"