Consider the following function. y= + -2x+8 3 2 (a) Find y' f'(x). f'(x) = x²+x-2 (b) Find the critical values. (Enter your answers as a comma-separated list.) x= -2,1 (c) Find the critical points. (x, y) = (-2, 34 3 (smaller x-value) - (x, y) = (1, 41 6 (larger x-value) (d) Find intervals of x-values where the function is increasing. (Enter your answer using interval notation.) (1,00) × Find intervals of x-values where the function is decreasing. (Enter your answer using interval notation.) (-2,1) (e) Classify the critical points as relative maxima, relative minima, or horizontal points of inflection. In each case, check your conclusions with a graphing utility. (If an answer does not exist, enter DNE.) relative maxima (x, y) = (-2, 34 3 relative minima (x, y) = horizontal points of inflection xxn-( 1, 41

Find f''(x) for the function. f(x) = 8x³ - 2x² +4 OA. 32x-4 B. 4x-32 C. 48x-4 OD. 4x-48

Differentiate the function G(x) = 6x-6 + 5x-9. Answer G'(x) =

Evaluate y' of the given functions:1. y+ (x2-2)(x+3)2. y = (x-4)/X2

Differentiate the function. h'(x) = h(x) = (x5 - 4x³ + 5)8 4 X

Find f. f"(x)  =20x3 -12x2 +6x

Find f. f"(x)  =x6 - 4x4 +x +1

Consider the following. f(x) = x³ = 6x² +8 (a) Find f'(x) and f"(x). f'(x) = F"(x) = (b) Graph f(x), f(x), and f"(x) with a graphing utility. y 150 100 50 XXX. -5 -50 -100 -150 x = -5 y 150 100 x = 50 -50 -100 -150 (c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.) 5 Identify x-values where F"(x) > 0. (Enter your answer using interval notation.) Identify x-values where f"(x) < 0. (Enter your answer using interval notation.) (d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your answers as a comma-separated list.) Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.) Identify x-values where f'(x) is decreasing. (Enter your answer using interval notation.) -5 y 150 100 50 -50 -100 -150 DO -5 y 150 1000 50 -50 -100 -150 X

Find the slope of the graph of the function f(x)=(-5x – 4)² at x = 3. a. f'(x)=-38 b. f'(x)=95 c. f'(x)=-13,718 d. f'(x)=110 e. f'(x)=190

Find f'(x) and simplify. f(x) = (0.2x + 2)(0.6x - 9) Which of the following shows the correct application of the product rule? A. (0.2x+2)(0.2) + (0.6x9)(0.6) O B. (0.2x + 2)(0.6) - (0.6x-9)(0.2) O C. (0.6)(0.2) D. (0.2x + 2)(0.6) + (0.6x-9)(0.2) f'(x) =