Find the following using the table below. X 1 2 3 4 f(x) 2 1 3 4 f'(x) 1 4 2 3 g(x) 2 1 4 3 g'(x) 2 3 4 1 h'(4) if h(x) = f(x) g(x) f(x) h'(4) if h(x) = g(x) h'(4) if h(x) = f(g(x))
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- If f(x) = x2/(1+ x) , find f" (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 XUse the values in the table below to answer each of the following: f(x) g(x) f'(x) g'(x) 5 X h'(4) = 4 8 16 4 3 7 Oh'(x) -2 = (a) Let h(x) = f(x²). Find h'(x). g(x) 3 = 1 Oh'(x) = -3 0 Oh'(x) 2xg(x) f'(x²)-f(x²) g'(x) (g(x))² -1 5 6 f(x²) g'(x)−g(x) f'(x²) (g(x))² · g(x) f'(x²)-f(x²) g'(x) (g(x))² ○ h'(x) = f(x²) g'(x)—2xg(x) f'(x²) (g(x))² which tells us that h(x) is ---Select--- at x = 4 . (b) Let p(x) = g(g(x)) . Find p'(x). Op'(x) = g'(g(x)) g'(x) Op'(x) = 2g'(g(x)) p'(x) = 2g'(g(x)) g(x)+g (g(x)) g(x) p'(x) = g'(g(x)) g(x)+g (g(x)) g(x) Op'(x) = g'(g(x))
- Let h(x) = f(x)g(x). If f(x) = -3x²+2x 3 and g(x) 3x" + 4x + 3, what is h' (1)? Do not include "h' (1) =" in your answer. For example, if you found h' (1) = 7, you would enter 7.Find each of the following. In some cases, you may need to rewrite the function first. (a) F'(x) for f(x) = ax¹¹ + cx + b F'(x) (b) g(x) for g(x) g(x) = A(X) 11 (c) h (x) for h(x) = 13e" - w'(x) 1 TE El (d) w (x) for w(x) = (1) 11 + (+)*+√If g(x) = (x^2 − 1)/(2x+1) , find g′(−1).