Find ▽f(x) and ▽2f(x) f(X) bXc, where X E RnXn and b, c E R". - 0AC. where Find ▽f(x) and ▽2f(x) f(X) bXc, where X E RnXn and b, c E R". - 0AC. where
53. Find f'(x) when f(x) = 3re". A. f'(x) = 3r%e* + 3x B. f'(x) = 3e C. f'(x) = 3e* + 3xe D. f'(x) = f* + 3x
3. Given f(x,y)= sin?(2x+3y?).e***; (a) Find f (x,y). (b) Find f (x,y).
Find the indicated derivative for the given function. f"(x) for f(x) = e = x2 {"(x) =
4. For this question, define f(x) = (x - 1)e-(0-1). (a) Find f'(x) and f"(x). (b) Find where S is increasing and where / is decreasing (e) Find where S is concave up and where / is concave down. (a) Find all critical points of . For each point you find, explain whether it is a (relative) maximum, a (relative) minimum or neither. (e) Find all points of inflection of f. For each point you find, explain why it is...
Find f'(x) and f''(x) for the following: f(x) = e^cos(2x^3) b) f(x) = 20 x^3 + 12 x^2 - 8x sin (7x)
2. Given f(x)=e*: (a) Find f'(x) using the definition of derivative, f'(x)= lim{{(x+h)-f(x)), by making h smaller and smaller. Round answer to two decimal places. (b) Evaluate f (1). (c) Carefully, graph f(x)=e-*, -15x52 using points every 0.5 units. (d) Find the equation of the tangent line at x = 1. Attach the graph of this line to the graph in (c).
Find f (x,y). f(x,y)= e - 4x + 3y A. fx(x,y)= -4 e - 4x OB. {x(x,y)= - 4 € -4x+3y OC. fx(x,y) = e -4x+3 OD. fx(x,y) = 3 e - 4x+3y
a) If f(0) = 5sec° 0 – sec°O + sec e Find: f'(0) b) If f(x)= xe * + In 8x3 +In( cos x) -2x e Find: f'O
(7) In this problem let X denote the vector space C(0, 1) with the sup norm. (a) Given f e X, define d(f) = f2. : X → X is differentiable, and Prove that φ find φ'(f). (b) Given f e X, define 9(f) = J0 [f(t)]2dt. Prove that Ψ : X → R is differentiable. and find Ψ(f). (7) In this problem let X denote the vector space C(0, 1) with the sup norm. (a) Given f e X,...