Question

(b) Find the equation for the tangent plane to the graph of $z = f(x, y) = y^2e^x$ at $(0, 1)$. Use this equation to approximate $f(0.2, 1.1)$.

Name: (b) Find the equation for the tangent plane to the graph of z = f(x, y) = y^2e^x at (0, 1). Use this equation to approximate f(0.2, 1.1).
Uploaded: 2020-08-22T19:11:39-08:00
Duration: 1 min 54 s
Channel: Linh Vu
Description: (b) Find the equation for the tangent plane to the graph of z = f(x, y) = y^2e^x at (0, 1). Use this equation to approximate f(0.2, 1.1).

          (b) Find the equation for the tangent plane to the graph of $z = f(x, y) = y^2e^x$ at $(0, 1)$. Use this equation to approximate $f(0.2, 1.1)$.

Added by Stacey T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linh Vu

08/22/2020

Step 1

f(x,y) = y^2 e^x, the base point is (x,y) = (0,1). Then f(0,1) = 1, so the point on the graph is (0,1,1). Show more…

Show all steps

Thanks for your feedback!

Hi, for this problem do I move Z to the other side of the equation before solving? z=f(x,y) and (x,y)=(0,1) and f(0,1)=1 so (x,y,f)=(0,1,1). Should I solve for the tangent plane using 0=f(x,y)-z and (0,1,1)? I did so by finding gradient f(x,y,z) at (0,1,1) using that as my normal vector, and the point (0,1,1) I got x+2y-z+3 as my tangent plane equation. Should I have solved it only in terms (x,y)? (b)Find the equation for the tangent plane to the graph of z =f,y=ye at 0,1. Use this equation to approximate f(0.2,1.1)