Concept explainers
HOW DO YOU SEE IT? The figure shows die graph of g'.
(a)
(b)
(c) What can you conclude about the graph of g knowing that
(d) What can you conclude about the graph of g knowing that
(e) Is
(f) Is it possible to find g(2) from die graph? Explain.
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Chapter 2 Solutions
Calculus of a Single Variable
- In a study on the speed of muscle contraction in a certain species of frogs under various loads, researchers found that the speed of contraction decreases with increasing loads. In particular, they found that the relationship between speed of contraction v (in centimeters per 25 +0.07x second) and load x (in grams) is given approximately by v(x) = - -, x>5. X (A) What does v(x) approach as x increases? (B) Sketch a graph of the function v. (A) As x increases, v(x) approachesarrow_forward3-4 Match each equation with its graph. Explain your choice: (Don't use a computer or graphing calculator.) 3. (a) y = x (b) y =x' (c) y = x* 0. f 4. (a) y = 3x (c) y = x' (b) y = 3* (d) y = Vx yA F Garrow_forwardThe graph of the functions f and g are shown below. 5 g(x) f(r) -5 5 (a) Let h(x) = f (x)/g(x). Find h'(1). (b) Let h(x) = g(f(x)). Find h'(-1).arrow_forward
- The graph of g(x) = x² was transformed to create the graph of h(x) = –-) . Which of these describes the transformation from the graph of g to the graph of h? A. reflection over the x-axis and a horizontal stretch B. A reflection over the y-axis and a horizontal stretch C. A reflection over the x-axis and a vertical stretch D. A reflection over the y-axis and a vertical stretcharrow_forwardA 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).arrow_forwardUse 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 Itarrow_forward
- Given the graph of y = f(x) sketch the graph of f'(x) ow 4 2 -2 -2arrow_forwardThe 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_forwardConsider the graph of the function g(x) given below. g(x) -2 B) If h(x) [Select] C) If i(x) [Select] = -4- A) If f(x) = xg(x), calculate f' (3). [ Select] - 2- 0 -2 X g(x) 2 9 calculate h' (-1). e f(x), calculate i” (1). X 4arrow_forward
- Sketch a graph of the function f(x)=0.5sin(3x)arrow_forward(a) Sketch the graph of f(x) = -(x - 1) + 1 along with the graph of y = f-(x). (b) Discuss what happens to the graph of y = f'(x) (in general) as the graph of y = f(x) is increasing or is decreasing. (c) What can you conclude about the intersection points of the graphs of a function and its inverse?arrow_forwardDifferentiate. g(x) = g'(x) = 5x − 1 6x + 5 + x3 ...arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,