(1 point) A student was asked to find the equation of the tangent plane to the s

Question

(1 point) A student was asked to find the equation of the tangent plane to the surface-,r-y3 at the point (?, ?)-(1 , 1 ). The student's answer was z-0 + 2x(x-I )-(3)2 ) (y-1). (a) At a glance, how do you know this is wrong. What mistakes did the student make? Select all that apply A. The (x 1) and (y - 1) should be x and y. B. The partial derivatives were not evaluated a the point. OC. The 0 should not be in the answer. D. The answer is not a linear function E. All of the above (b) Find the correct equation for the tangent plane.

Explanation / Answer

z = x2- y3

Partial derivatives are

fx (x,y) = 2x , fy (x,y) = -3y2

At point (1,1)

fx (1,1) = 2, fy(1,1) = -3

SO the mistake , the student made is

      B. The partial derivative were not evaluated at the point .

      Required equation of tangent is

b . z= 2(x-1)-3(y-1)

     z= 2x-3y +1

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