Original function: x^2 - y^2 Point of interest: (-2, -3) The graph includes: The

Question

Original function: x^2 - y^2 Point of interest: (-2, -3)
The graph includes: The graph includes: The unit vector in the direction of the gradient vector with starting point (-2,-3) and ending point (-2 -2/sqrt[13]), -3 + 3/sqrt[13]). Maximum rate of change: 2 sqrt [13]. F(-2,-3) = -5 The question again is: How does the GRAPH help interpretation of the maximum rate of change at this point. AxesLabel x, y), Axes True, contourshading Letiqueta de ejes Lejes verdad sombreado de contornos Show [ContourGraph2 Point of InterestUV, Gradunitvect muestra 00) iii) The graph shows that the output of the function at (-2, -3) is -5. 114) f [-2, 31 ut(114)as -5

Explanation / Answer

The direction in the graph is given by the gradient of the function. For the function: x^2 - y^2, the partial derivative with respect to x gives the rate of change of the function in the x direction and the partial derivative with respect to y gives the rate of change of the function f in the y direction. So in this case F(-2,-3) = -5.

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