The graphs of the functions f and g are shown in the figure. y 4 3. 'f 2 g 1 -1 1 2 3 4 Let u(x) = f(x)g(x) and v(x): f(x) = g(x) (a) Find u'(1). (b) Find v'(5). 10 5 6 x ©
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- If xis large, which function grows faster, f(x)=2x or g(x)=x2?Consider the function. g(x) = 2x4 - 5x³ + 13x – 3 Find g'(x). gʻ(x) = 8x – 15x2 + 13 Find g"(x). g"(x) = 5 Find g"(1) and g" 2 g"(1) 어(금)- o() 2 IIThe 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.)
- The function g(x) is obtained by shifting the graph of y=x2. (a) If g(3)=36, give a possible formula for g when g is the result of applying only a horizontal shift to y=x^2.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 XSketch the graph of f(x) = xª – 2.x² + 7 using graphing strategy (analyze f, f' and f").
- Use the graph of f and g. p(x) = f(x)g(x) f(x) q(x) = g(x) y 12 10 8 6 4 2 X -2 2 4 6 8 10 -21 (a) Find p'(4). p'(4) = (b) Find q'(7). q'(7) = Need Help? Read ItIf f(x) = 3x² - x³, find f'(x), ƒ''(x), ƒ'''(x), and f(4)(x). f'(x) = f"(x) = f'(x) = f(4) (x) = Graph f, f', f", and f"" on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives? The graphs ---Select--- consistent with the geometric interpretations of the derivatives because f' ---Select--- --Select--- ✓where f' has a slope of m = 0, and f"" is ---Select--- ✓function equal to the slope of f". ✓where f has a slope of m = 0, f"A 57. (a) Graph the function f(x) = x - 3x - 6x2 + 7x + 30 in the viewing rectangle [-3, 5] by [-10, 50]. (b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of f'. (See Example 2.2.1.) (c) Calculate f'(x) and use this expression to graph f'. Compare with your sketch in part (b).
- The graph of the function f(x) is shown below. It consists of a semicircle and two straight line segments. 150 + -3 -2 y 3 2 -1 1 2 (b) Which of the following numbers is the smallest: ƒ' (−3.95), ƒ' (−1.5), ƒ' (−0.05), ƒ' (1), ƒ' (3.05)? 3 5 XUse the graph of f and g. p(x) = f(x)g(x) f(x) q(x) g(x) y 12 10 8 2 -2 4 6. 8 10 (a) Find p'(4). p'(4) = (b) Find q'(7). q'(7) =Assume that the function f is a one-to-one function. (a) If f(5) = 2, find f-'(2). Your answer is (b) If ƒ-( – 4) 4, find f( – 4). Your answer is If f(x) = x + 7 and g(x) = x – 7, (a) f(g(x)) = 1 (b) g(f(x)) (c) Thus g(x) is called an function of f(x) S PhotoGrid
