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- 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 XFind g'(x) for the given function. Then find g'(-4), g'(0), and g'(2). g(x)=√15xIf g(x) = (x^2 − 1)/(2x+1) , find g′(−1).
- Use the graph of f and g. p(x) = f(x)g(x) g(x) = f(x) g(x) -2 10- 8 6 2 0 (a) Find p'(8). p'(8) = (b) Find q'(1). q'(1) = 2 4 X f 8 g 10Given f(-6) = 17,ƒ'(-6) = -2, g(-6)= -3, and g'(-6)= 2, find the value of h'(-6) based on the function below. h(x) = f(x) g(x) h'(- 6) = Keypad Keyboard ShortcutsUse the graph of f and g. p(x) = f(x)g(x) f(x) g(x) q(x) 10 2 -2 2 6 10 -2 (a) Find p'(9). p'(9) = (b) Find q'(1). q'(1) = %3D 4.
- Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Y'(I) = Function y = 5 + csc(x) 9-csc(x) Point AFind 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)=190Consider 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)