4) The graph of the derivativef'of a functionf is shown.(a) On what interval(s) is f increasing?(b) At what value(s) of x does f have a local maximum?(c) On what interval(s) is f concave up?(d) What is/are the x-coordinate(s) of the inflection point(s) off?y = f'(x)Ar6(e) If the given graph represents the velocity graph of a particle, on what intervals is the particle speeding upand slowing down?

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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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The graph of the derivative of a function f is shown to the right. The graph has horizontal tangent lines at x = -1, x= 1, and x = 3. At which of the following values of x does f have a relative maximum? (A) -2 only 3+ (В) -2, 1, and 4 2+ (C) 4 only (D) -1 and 3 only -1 Graph of f' Pictured to the right is the graph of h' (x) , the derivative of a function, h(x). Which of the following statements is/are true? Graph of h'(x) I. The graph of h(x) has a horizontal tangent when x = 3. II. The graph of h(x) is increasing on the interval (-∞, 2). - -2 1 1 2 4 III. The graph of h(x) is decreasing on the interval (-∞0, 3). (A) I only (В) П only (C) I and II only (D) I and III only The function f has the property that f(x),f'(x), and f"(x) are negative for all real values of x. Which of the following could be the graph of f? (A) (В) (C) (D) (E)
Let f be the function f(z) = 6 - - 4 +8.- 5. Calculate the first, second, and third derivatives of f. f'(=) - S"(r) - f"(2) - Check
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The duration of daylight L in minutes(sunrise to sunset), x kilometers north of the equator on May 17, is given by the function L=f(x). What are the units of measurement of the second derivitive f"(4000)? a)kilometers/minute b)minutes/kilometer c)kilometers/minute^2 d) minutes/kilometer^2 e) minutes^2/kilometer^2 The derivative of a function is NEGATIVE everywhere on the interval x = 2 to x = 3. Where on this interval does the function have its maximium value? a). At x = 2 b) At x = 3 c.) Somewhere between x = 2 and x = 3 d) It does not have a maximium since the derivative is never zero e) We cannot tell if it has a maximium since we don't knw where the second derivative is negetive.
Suppose that for a certain function f' (5) Test, f(5) is a = 0 and f " (5) = – 1. . Then, using the Second maximum. Derivative, absolute Extrema, relative Derivative, relative Extrema, absolute
Analyze and sketch a graph of the function f(x)=xtan x over the interval -3pie/2<x < 3pie/2. Find teh f'(x) and f"(x). Find all intercepts, asymptoes, relative extrema and points of inflection.
Consider the function f(x) = a) What is the slope of the tangent line at the point (1, -2)? What is the equation of the tangent line at the point (1, -2)? m = y = b) There is a point (a, b) on the graph of x² f(x) = a = x² - 5 x² + 1 - y = 5 x² + 1 horizontal. Input the value of a and the equation of the tangent line: for which the tangent line is You may explain your answer below if you like (optional).
If the slope of the graph of f (same as slope of tangent line to graph of f), at the point (1, 2), is 7, then what point is on the graph of f'? O (1,7) can't be determined O (7,1) O (2,7) O (7,2)

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4) The graph of the derivativef'of a function) IS (a) On what interval(s) is f increasing? (b) At what value(s) of x does f have a local maximum? (c) On what interval(s) is f concave up? (d) What is/are the x-coordinate(s) of the inflection point(s) off? व y = f'(x) Ar