4) (15 pts) Given f(x) = -3xº + 5x3 + 3x + V5, calculate f'(x). 5)...
Question 1. (15 pts) Given f(x,
y) = 3x 2 + y 3 . (a) Find the gradient of f. (b) Find the
directional derivative of f at P0 = (3, 2) in the direction of u =
(5/13)i + (12/13)j.
Question 1. (15 pts) Given f(L,y) = 3x2 +y?. (a) Find the gradient of f. (b) Find the directional derivative off at P =(3,2) in the direction of u=(5/13)i + (12/13)j.
Q1. f(x) = 5x3 – 2x² + 3x is given. a) Find the critical points of f(x). b) Find the intervals where f(x) increases/decreases. c) Classify the critical points of f(x). d) Find the intervals where f(x) is concave up/down. e) Find the inflection points of f(x).
Match the function operation below with its result given that f(x)=x^,g(x)= - 3x?, and h(x) = 3.3Vx. x)=x7.00) = -3x2,ama ncx) = 3.3V2 A. -3x (g)(81) (f + h)(x) B. N| با (x) c. -2.3x (f-h)(x) D.-18.4 (f + h)(1) E. 4.3 (g)(x) F. -729 (16) G. 4.3x (f-h)(16) H.
Need help with functions.
f(x) = V5-x -5 -4 -3 -2 -1 i 2 -2y=h(x) a) f(-4)= d) (h/g)(-2) = b) x so that h(x) = 4. e) f(g()) = c) 2h(4)-f(1)+8 (2) f) g(h(4)) =
5x² + x 7) (15 pts) Given f(x) = calculate f'(x). 5-435
3) (15 pts) Given h(x) = -5x2 + 3x + 2, find the equation of the tangent line at x = -2. (Hint: For the tangent line at x = a, find f(a), and f'(a).)
1 2) (15 pts) Given g(x) g(x+h)-g(x) use the formula g'(x) = lim 6x+3' h0 h to find g'(x). 3) (15 pts) Given h(x) = -3x2 + 5x + 2, find the equation of the tangent line at x = -2. (Hint: For the tangent line at x = a, find f(a), and f'(a).)
Problem 4.1 Dependent equations? Given: x +2x2 2x+3x, 5 2xx +3x-2x 18 -x, + 3x2 + x3-4x,--6 x 3x2+ 5x 5x, 13 If the set of 4 equations is dependent or independent Find:
7) (15 pts) Given f(x) 4x2+x 6-3x4 calculate f'(x).
Given that f(x) = 3x + 1 g(x) = 5x - 8 and h(x) = 2x – 1 3 Find:- i) f(-4) = ii) g[h(5)] = iii) f[g(3)] = iv) g[h(x)] = vi) h-1(7) =