Find the following using the table below. X 12 3 4 f(x) f'(x) g(x) g'(x) 888 4424 3 1 2 4 3 1 2 23 1 4 3 2 1 h'(3) if h(x) = f(g(x))

Find h(x) if h'(x) h(x) = = 9x (3-x²)² and h(1) -3. ==

Consider the function f(x) = (g(x)h(x))^2 and the following function values: f(5) = 1 g(5) = −1 h(5) = 2 g' (5) = 3 h'(5) = 4 Find f'(5)

Find f"(x) for the equation f(x)=x6(x2-1)3

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 h(x) if h'(x) h(x) = = 5x (6 - x²)² X and h(1) = : -6.

For the function, find the following. f(x) = x4 − 7x3 − 3x2 + 9x − 4   (a)    f '(x)   (b)    f ''(x)   (c)    f '''(x)   (d)    f (4)(x)

Consider the function f(x) = exact values. f'(x) = f’’(2) = f'''(x) = = - 2x - 5 x - 1 Compute each of the following. Simplify your answer and use .

x + 2 Consider the function f(x) Compute each of the following. Simplify your answer and use exact 3 values. f'(x) f"(x) = f''(x) =

3x + 1 Consider the function f(x) Compute each of the following. Simplify your answer and use x – 3 exact values. f'(x) = f'"(x) = f'''(x)