Given the graph of a function z = f(x, y) and its traces in the planes x = 4, y = 1, and y = 3 (see figure), determine whether the following partial derivatives are positive or negative. ZA z= fr, y) 3 a. f.(4, 1) b. f,(4, 1) c. f,(4, 3) d. f,(4, 3)

Q: The intersections with the abscissa axis of the image function are: f (x) = x2 + 10x + 21

A:

Q: Use the Chain Rule to find the indicated partial derivatives. N=D+q p+r p=u+vw, q=v+uw, r=w+ Uv; an…

A: Given:  N=p+qp+r, p=u+vw, q=v+uw, r=w+uv We have to ∂N∂u, ∂N∂v, ∂N∂w, when u=9, v=2, w=3.

Q: ind the slope in the x-direction at the at P(0, 2, ƒ(0, 2)) on the graph of f when f(x, y) slope = 0…

A: We will find the required.

Q: Use the chain rule to find the indicated partial derivatives. p+q N = -, p = u + vw, q = v + uw, r =…

A:

Q: 144y+312y+ 169y= 0. y(0) = 6. (0) = 6. %3D %3D

A: Let the given differential equation be, 144y''+312y'+169y=0 Assume the solution of the differential…

Q: Consider the following R2 →R function:  b) Plot the level curves for c = 0, 1, 2 and 3

A: