77 lines
4.0 KiB
XML
77 lines
4.0 KiB
XML
<svg width="440" height="190" xmlns="http://www.w3.org/2000/svg">
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<defs>
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<marker id="cn-arr" markerWidth="7" markerHeight="5" refX="7" refY="2.5" orient="auto">
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<path d="M0,0 L7,2.5 L0,5" fill="#ccc"/>
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</marker>
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</defs>
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<!-- === Convex (bowl) === -->
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<text x="70" y="14" text-anchor="middle" fill="#333" font-size="10" font-weight="bold">Convex (f'' > 0)</text>
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<line x1="10" y1="145" x2="135" y2="145" stroke="#ccc" stroke-width="0.8" marker-end="url(#cn-arr)"/>
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<line x1="10" y1="145" x2="10" y2="22" stroke="#ccc" stroke-width="0.8" marker-end="url(#cn-arr)"/>
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<!-- Bowl curve -->
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<path d="M 15,40 Q 45,125 70,140 Q 95,125 125,40" fill="none" stroke="#27ae60" stroke-width="2.5"/>
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<!-- Line segment above curve -->
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<line x1="30" y1="95" x2="112" y2="95" stroke="#27ae60" stroke-width="1" stroke-dasharray="3"/>
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<circle cx="30" cy="95" r="2.5" fill="#27ae60" fill-opacity="0.5"/>
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<circle cx="112" cy="95" r="2.5" fill="#27ae60" fill-opacity="0.5"/>
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<text x="71" y="88" text-anchor="middle" fill="#27ae60" font-size="8">line above curve</text>
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<!-- Min point -->
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<circle cx="70" cy="141" r="4" fill="#27ae60"/>
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<text x="70" y="160" text-anchor="middle" fill="#27ae60" font-size="9" font-weight="bold">minimum</text>
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<text x="70" y="172" text-anchor="middle" fill="#27ae60" font-size="8">curves upward</text>
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<!-- Divider 1 -->
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<line x1="148" y1="10" x2="148" y2="175" stroke="#ddd" stroke-width="1" stroke-dasharray="4"/>
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<!-- === Concave (hill) === -->
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<text x="220" y="14" text-anchor="middle" fill="#333" font-size="10" font-weight="bold">Concave (f'' < 0)</text>
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<line x1="160" y1="145" x2="285" y2="145" stroke="#ccc" stroke-width="0.8" marker-end="url(#cn-arr)"/>
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<line x1="160" y1="145" x2="160" y2="22" stroke="#ccc" stroke-width="0.8" marker-end="url(#cn-arr)"/>
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<!-- Hill curve -->
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<path d="M 165,135 Q 195,45 220,30 Q 245,45 275,135" fill="none" stroke="#e74c3c" stroke-width="2.5"/>
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<!-- Line segment below curve -->
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<line x1="182" y1="85" x2="260" y2="85" stroke="#e74c3c" stroke-width="1" stroke-dasharray="3"/>
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<circle cx="182" cy="85" r="2.5" fill="#e74c3c" fill-opacity="0.5"/>
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<circle cx="260" cy="85" r="2.5" fill="#e74c3c" fill-opacity="0.5"/>
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<text x="221" y="100" text-anchor="middle" fill="#e74c3c" font-size="8">line below curve</text>
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<!-- Max point -->
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<circle cx="220" cy="30" r="4" fill="#e74c3c"/>
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<text x="220" y="160" text-anchor="middle" fill="#e74c3c" font-size="9" font-weight="bold">maximum</text>
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<text x="220" y="172" text-anchor="middle" fill="#e74c3c" font-size="8">curves downward</text>
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<!-- Divider 2 -->
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<line x1="298" y1="10" x2="298" y2="175" stroke="#ddd" stroke-width="1" stroke-dasharray="4"/>
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<!-- === Inflection point === -->
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<text x="370" y="14" text-anchor="middle" fill="#333" font-size="10" font-weight="bold">Inflection (f'' = 0)</text>
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<line x1="310" y1="145" x2="435" y2="145" stroke="#ccc" stroke-width="0.8" marker-end="url(#cn-arr)"/>
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<line x1="310" y1="145" x2="310" y2="22" stroke="#ccc" stroke-width="0.8" marker-end="url(#cn-arr)"/>
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<!-- S-curve transitioning concave to convex -->
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<path d="M 315,30 Q 340,40 355,65 Q 370,90 370,90 Q 370,90 385,115 Q 400,135 430,140" fill="none" stroke="#9b59b6" stroke-width="2.5"/>
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<!-- Inflection point -->
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<circle cx="370" cy="90" r="4" fill="#9b59b6"/>
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<!-- Tangent at inflection -->
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<line x1="340" y1="110" x2="400" y2="70" stroke="#9b59b6" stroke-width="1.2" stroke-dasharray="4"/>
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<!-- Labels for concave/convex regions -->
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<text x="340" y="45" fill="#e74c3c" font-size="8">concave</text>
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<text x="400" y="138" fill="#27ae60" font-size="8">convex</text>
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<text x="370" y="160" text-anchor="middle" fill="#9b59b6" font-size="9" font-weight="bold">switches here</text>
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<text x="370" y="172" text-anchor="middle" fill="#9b59b6" font-size="8">curvature changes sign</text>
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<text x="220" y="187" text-anchor="middle" fill="#666" font-size="10">convex: bowl (unique min) | concave: hill (unique max) | inflection: curvature flips</text>
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</svg>
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