A student was asked to find the equation of the tangent plane to the surface z =

Question

A student was asked to find the equation of the tangent plane to the surface z = x^4 - y^5 at the point (x, ;y) = (5, 3). The student's answer was z = 382 + 4x^3(x - 5) - (5y^4)(y - 3). At a glance, how do you know this is wrong. What mistakes did the student make? Select all that apply. The partial derivatives were not evaluated a the point. The 382 should not be in the answer. The (x - 5) and (y - 3) should be x and y. The answer is not a linear function. All of the above Find the correct equation for the tangent plane. Z =

Explanation / Answer

a)option A,D

z=x4-y5

(x,y)=(5,3)

zx=4x3 ==>zx(5,3)=4*53=500

zy=-5y4==>zy(5,3)=-5*34=-405

z(5,3)=54-35 =382

euation of tangent plane is z-382=zx(x-5)+zy(y-3)

z-382=500(x-5)-405(y-3)

z=382+ 500(x-5)-405(y-3)

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