Partial Derivatives, Tangent Plane, and Gradient
2015-01-06 01:43
This applet demonstrates the geometric meaning of partial derivatives, tangent planes, and gradient vectors for multivariable functions. Users can interactively observe tangent plane variations at specific points and explore the relationship between gradient vectors and contour lines, providing an intuitive understanding of core calculus concepts.
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<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="txtGrad" exp=""∇f""/>
<element type="text" label="txtGrad">
<show object="true" label="false" ev="37"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="23" y="95"/>
<ggbscript val="SetValue[showGrad, !showGrad]"/>
</element>
<expression label="text3" exp=""∇f""/>
<element type="text" label="text3">
<show object="true" label="false" ev="37"/>
<condition showObject="showGrad"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint exp="Q + vg"/>
<labelOffset x="-30" y="-5"/>
</element>
<expression label="txtFx" exp=""f_x""/>
<element type="text" label="txtFx">
<show object="true" label="false" ev="37"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="192" b="203" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="23" y="57"/>
<ggbscript val="SetValue[showFx, !showFx]"/>
</element>
<element type="boolean" label="showFx">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
</construction>
</geogebra>