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Section 13.3 : Interpretations of Partial Derivatives
- Determine if \(f\left( {x,y} \right) = x\ln \left( {4y} \right) + \sqrt {x + y} \) is increasing or decreasing at \(\left( { - 3,6} \right)\) if
- we allow \(x\) to vary and hold \(y\) fixed.
- we allow \(y\) to vary and hold \(x\) fixed.
- Determine if \(\displaystyle f\left( {x,y} \right) = {x^2}\sin \left( {\frac{\pi }{y}} \right)\) is increasing or decreasing at \(\displaystyle \left( { - 2,\frac{3}{4}} \right)\) if
- we allow \(x\) to vary and hold \(y\) fixed.
- we allow \(y\) to vary and hold \(x\) fixed.
- Write down the vector equations of the tangent lines to the traces for \(f\left( {x,y} \right) = x\,{{\bf{e}}^{2x - {y^{\,2}}}}\) at \(\left( {2,0} \right)\). Solution