Compute the following.
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- 3. Find g if g'(x) = 8x(x® – ) and g(2) = 3.arrow_forwardDetermine h(1) and h'(1). h(x) = [f (x)]2arrow_forwardLet f and g be functions that satisfy f'(2) = -6 and g'(2) = 9. Find h'(2) for each function h given below: (A) h(æ) = 6f(x). h'(2) = -36 (B) h(x) = -59(x). h'(2) = (C) h(x) = 8f(x) + 13g(x). h'(2) = (D) h(x) = 12g(x) – 11f(x). h'(2) = %3D (E) h(x) = 10f(x) + 9g(x) – 2. h'(2) = (F) h(x) = – 10g(x) – 3f(x) – 2x. h'(2) =arrow_forward
- Suppose that for the functions f(x) and g(x), f'(x) = g'(x) on [10, 12] ƒ(10) = 9 g(10) = -9 ƒ(12) = 11 What is the value of g(12)? Provide your answer below: g(12)=arrow_forward2. Determine f'(1) for the function f (x) = (8x – 6Vx5 +3)(x7 – +arrow_forwardConsider 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 Xarrow_forward
- Suppose that f(x) and g(x) are two functions and we know that: f(-3) = 2 g(-3) = 5 f'(-3) g'(-3) Find the following: (ƒ − g)'(−3) = (g - f)'(-3) = -1 -2 == (fg)'(-3) = (4) - '(-3) = f(x) x² If k(x) = = = then k'(-3)arrow_forwardLetf, g be functions. Suppose we know that ƒ(−6) = 4, ƒ'(−6) = −4, g(−6) = −4, g′(−6) = −3. Using the above information, compute h' (-6) where h(x) = (f(x))² g(x). h'(- 6) = Numberarrow_forwardIf f(x) = 20 X compute f(2) and f'(2).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage