Find an equation for the plane tangent to the surface given by z = x 2 + y 4 + e xy at the point (1, 0, 2).

Step-by-step explanation:

Let

                               .

The partial derivatives of this function are

The tangent plane equation through a point is given by                    

In this case, we have

The values of the partial derivatives in this point are

So, the equation is

Therefore, the equation for the plane tangent to the surface at the point is given by

b

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)