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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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).
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"
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 II
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.)
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)

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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)