Question

The equation of the tangent plane to the graph of the function f(x,y)=x−y²/2 at (2,4,−6) is:

A. 2x+y+z=2
B. x+4y=18
C. x−4y−z=−4
D. −x+4y+z=8
E. x-y-2z = 10

Answer 1

The equation of the tangent plane to the graph of the function f(x,y)=x−y²/2 at (2,4,−6) is x - 4y - z = -4.

Step-by-step explanation:

The equation of the tangent plane to the graph of the function f(x,y)=x-y²/2 at (2,4,-6) can be found using the formula for a tangent plane. The formula is given by:

z - z1 = fx(x1,y1)(x - x1) + fy(x1,y1)(y - y1)

First, we find the partial derivatives of f(x,y) with respect to x and y:

fx(x,y) = 1

fy(x,y) = -y

Plugging in the values (2,4,-6) and evaluating the derivatives, we get the equation of the tangent plane as x - 4y - z = -4, which corresponds to option C.