177. The graph of a function f, which consists of two line segmentsXand a quarter circle, is pictured to the right. If H(x) = f()dt,which of the following statements is true?A. H(4) < H'(2) < H" (3)VB. H(4)

As per the Fundamental theorem of calculus, the derivative of the given function will be given…

Answered: 7. The graph of a function f, which…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Sketch the graph of a function with the following properties: • f'(x) > 0 when x 5 f'(2) = 0 and f'(5) = 0 •f"(x) 0 when 2 7 ● . • f(0) = -4 . 3 1 2 3 4 5
The graph y = f(x) is given, Sketch the graph of y = f'(x) on top of the graph and sketch y = f"(x) on the second graph .Clearjy label the coordinates of the x-intercepts of each graph.
If 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"
Use the graphs of f and g. Let p(x) = f (x)g(x) and q(x) = f (x)/g(x).
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.)
Letf, 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) = Number
If f'(x) = 3€¯X +1,on what interval(s), if any, is the graph of f(x) increasing? A. (-x,0) B. (-0,-3) c. (-3,0) D. Never, f(x)is always decreasing

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7. The graph of a function f, which consists of two line segments and a quarter circle, is pictured to the right. If H(x) = c) = f(d, which of the following statements is true? A. H(4) < H'(2) < H"(3) B. H(4) H"(3) < H'(2) C. H'(2) < H(4) < H"(3) D. H"(3)