Chapter 4: Partial Differentiation
Section 4.5: Gradient Vector
At P:2,1, determine the maximal rate of change and its direction for fx,y=x yx2+y3.
At P:2,1, the direction of the maximal rate of change of f is ∇fP/∥∇fP∥ = 15−34.
The maximal rate of change itself is ∇fP=1/5.
Maple Solution - Interactive
Student Multivariate Calculus
Control-drag the expression defining f.
Context Panel: Student Multivariate Calculus≻Differentiate≻Gradient
Complete the Gradient dialog as shown in Figure 4.5.11(a).
Context Panel: Select Element≻1
Context Panel: Assign to a Name≻GfP
Figure 4.5.11(a) Gradient dialog
x yx2+y3→gradient−325425→select entry 1−325425→assign to a nameGfP
Write the name GfP.
Context Panel: Evaluate and Display Inline
Context Panel: Normalize≻Euclidean
GfP = −325425→Euclidean-normalize−3545
Context Panel: Norm≻Euclidean
GfP = −325425→Euclidean-norm15
Maple Solution - Coded
Install the Student MultivariateCalculus package.
Use Gradient command.
Apply the Normalize command.
NormalizeGfP = −3545
Apply the Norm command.
NormGfP = 15
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