Suppose f(x, y)=xy, p=(−4,−4) and v=2i+3j. a. find the gradient of f. ∇f= i+ j note: your answers should be expressions of x and y; e. g. "3x - 4y" b. find the gradient of f at the point p. (∇f)(p)= i+ j note: your answers should be numbers c. find the directional derivative of f at p in the direction of v. duf= note: your answer should be a number d. find the maximum rate of change of f at p. note: your answer should be a number e. find the (unit) direction vector in which the maximum rate of change occurs at p. u= i+ j note: your answers should be numbers

a) The gradient of a function is the vector of partial derivatives. Then

b) It's enough evaluate P in the gradient.

c) The directional derivative of f at P in direction of V is the dot produtc of and v.

d) The maximum rate of change of f at P is the magnitude of the gradient vector at P.

e) The maximum rate of change occurs in the direction of the gradient. Then

is the direction vector in which the maximum rate of change occurs at P.

here is the

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b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5