Compute the following.
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
CALCULUS+ITS APPL.,BRIEF-MYLAB MATH
- The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). y 15 10 5 -2 4 6. 10 (a) Write an equation for h'(x) in terms of f(x), g(x), f'(x), and g'(x). O h'(x) = g'(f'(x))f'(x) O h'(x) = g'(f(x))f'(x) h'(x) = f'(g'(x))g'(x) h'(x) = f'(g(x))gʻ(x) O h'(x) = f'(g'(x))g(x) O h'(x) = g'(f'(x))f(x) Find h'(3). (If an answer does not exist, enter DNE.) (b) Write an equation for s'(x) in terms of f(x), g(x), f'(x), and g'(x). O s'(x) = f'(g(x))g'(x) O s'(x) = g'(f'(x))F'(x) O s'(x) = f'(g'(x))g'(x) s'(x) = g'(f(x))f'(x) s'(x) = f'(g'(x))g(x) s'(x) = g'(f'(x)){x) Find s'(7). (If an answer does not exist, enter DNE.)arrow_forward(a) Consider the ARMA(2,1) process {Xt}, Xt = 0.45Xt-1 − 0.05Xt-2 + €t - 0.2€t-1 where t~ iid(0, 0²).arrow_forwardFind g′(5)arrow_forward
- 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_forwardSuppose 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_forward
- Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown. F G (a) Find P '(2). (b) Find Q'(7).arrow_forwardLet 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.arrow_forwardLet f(x) and g(x) be functions whose graphs are shown below. Which of the following statements is/are true? I. If h(x) = f(x)+ g(x), then h'(2) is negative. II. If h(x) = f(x)g(x), then h'(2) = 0. f(x) III. If h(x) = g(x)' then h'(2) is positive. 6xy f(x) شا 5 4 3 2 1 A. I only B. III only C. II and III only 9(x) 1 2 3 4 5 6 7 MacBook Pro 2x8arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage