You are standing at the point (1,1,3) on the hill whose equation is given by z =

ID: 2968619 • Letter: Y

Question

You are standing at the point (1,1,3) on the hill whose equation is given by z = 5y - x^2 - y^2.

(a) If you choose to climb in the direction of steepest ascent, what is your initial rate of ascent relative to the horizontal distance?

The answer for (a) I think is the gradient vector of z. Is this right? If I'm right the answer is grad z = -2i + 3j. Please let me know if I'm wrong.

(b) If you decide to go straight northwest, will you be ascending or descending? At what rate?

So what I think is that north is + x direction and west is - y direction, So I think it is ascending.

The rate is the dot product of grad Z and unit vector of NW, so i think it is (5/sqrt{2}) . Please let me know if I'm wrong.

I have no idea in this question.

f(x) = -x^2 +5y-y^2-z

steepest ascent direction :

f'x. i + f'y. j+ f'z k

f'x = -2x = -2

f'y = 5-2y = 3

f'z = -1

steepest ascent direction = -2i+3j-k

)

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.