f(x, y, z) = √x + yz, P(1, 1, 3), u = <3/7, 2/7, 6/7> (a) Find the gradient of f. Vf(x, y, z) = < (b) Evaluate the gradient at the point P. Vf(1, 1, 3) = < (c) Find the rate of change of f at P in the direction of the vector u. Duf(1, 1, 3) =

find the gradient of the function at the given point. Then sketch the gradient together with the level curve that passes through the point f(x,y) = y - x, (2, I) Need Solution through 15min

Find the gradient of the function g(x,y) = xy at the point (4, - 4). Then sketch the gradient together with the level curve that passes through the point. First find the gradient vector at (4, - 4). Vg(4, - 4) =i (Di (Simplify your answers.) li +

find the gradient of the function at the given point. Then sketch the gradient together with the level curve that passes through the point. g(x, y) = x2/ 2-y2/2,(sqrt(2),1)

Find the gradient of the function at the given point. Function Point f(x, у, 2) x² + y2 + z2 (4, 2, 9) Vf(4, 2, 9) = Find the maximum value of the directional derivative at the given point.

flx.y)=X P=(-3,;4h V=2-23 A. Find the gradient of f. Vf = 1/y i+ -x/y^2 Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (Vf) (P) -1/4 i+ 3/16 Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf = (-7sqrt2)/32 Note: Your answer should be a number D. Find the maximum rate of change of f at P. 5/16 Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. i+ Note: Your answers should be numbers

f (x) = x² 2x + 2 P 3 3+ h Find an expression for the gradient of the line joining the points, P and Q.