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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Find the slopes of the surface f ( x ,   y )   =   4 x 2 + 9 y 2 + 36 at the point (1, - 1, 49) in

a. the x-direction.

b. the y-direction.

(a)

To determine

To calculate: The slope of the surface f(x,y)=4x2+9y2+36 in x direction at the point (1,1,49).

Explanation

Given information:

The provided function is f(x,y)=4x2+9y2+36 and the point is (1,1,49).

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided function is,

f(x,y)=4x2+9y2+36

Partially derivative of the function f(x,y)=4x2+9y2+36 with respect to x

(b)

To determine

To calculate: The slope of the surface f(x,y)=4x2+9y2+36 in y direction at the point (1,1,49).

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