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images/difference_quotient.svg

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+<svg width="380" height="200" xmlns="http://www.w3.org/2000/svg">
+  <defs>
+    <marker id="dq-arr" markerWidth="7" markerHeight="5" refX="7" refY="2.5" orient="auto">
+      <path d="M0,0 L7,2.5 L0,5" fill="#ccc"/>
+    </marker>
+  </defs>
+
+  <!-- Axes -->
+  <line x1="40" y1="170" x2="350" y2="170" stroke="#ccc" stroke-width="1" marker-end="url(#dq-arr)"/>
+  <line x1="40" y1="170" x2="40" y2="15" stroke="#ccc" stroke-width="1" marker-end="url(#dq-arr)"/>
+
+  <!-- Curve -->
+  <path d="M 55,145 Q 110,150 150,120 Q 195,85 240,60 Q 290,38 340,30"
+        fill="none" stroke="#9b59b6" stroke-width="2.5"/>
+
+  <!-- Point a -->
+  <circle cx="150" cy="120" r="4" fill="#e74c3c"/>
+  <line x1="150" y1="120" x2="150" y2="170" stroke="#e74c3c" stroke-width="0.8" stroke-dasharray="3"/>
+  <text x="145" y="183" fill="#e74c3c" font-size="10" text-anchor="middle">a</text>
+  <text x="138" y="115" fill="#e74c3c" font-size="9">f(a)</text>
+
+  <!-- Point a+h (far) - secant line -->
+  <circle cx="270" cy="47" r="4" fill="#999" fill-opacity="0.5"/>
+  <line x1="270" y1="47" x2="270" y2="170" stroke="#999" stroke-width="0.8" stroke-dasharray="3"/>
+  <text x="265" y="183" fill="#999" font-size="10" text-anchor="middle">a+h</text>
+  <line x1="110" y1="140" x2="310" y2="27" stroke="#999" stroke-width="1.5" opacity="0.4"/>
+  <text x="295" y="22" fill="#999" font-size="9">secant</text>
+
+  <!-- Point a+h (medium) -->
+  <circle cx="220" cy="70" r="4" fill="#999" fill-opacity="0.7"/>
+  <line x1="100" y1="145" x2="290" y2="35" stroke="#999" stroke-width="1.5" opacity="0.6"/>
+
+  <!-- Tangent (limit) -->
+  <line x1="80" y1="155" x2="280" y2="42" stroke="#3498db" stroke-width="2.5"/>
+  <text x="282" y="50" fill="#3498db" font-size="10" font-weight="bold">tangent</text>
+
+  <!-- Arrow showing h shrinking -->
+  <path d="M 265,160 Q 240,155 225,160" fill="none" stroke="#27ae60" stroke-width="1.2"/>
+  <path d="M 220,155 Q 195,150 175,155" fill="none" stroke="#27ae60" stroke-width="1.2"/>
+  <text x="200" y="150" fill="#27ae60" font-size="9" text-anchor="middle">h → 0</text>
+
+  <text x="190" y="198" text-anchor="middle" fill="#666" font-size="10">as h shrinks, secant → tangent</text>
+</svg>