25. Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1, and x = 2. There are horizontal tangents at x = -1.5 and x = 1.5.Which of the following statements is true?(-1.5, 13.1)-3.2 -2.4 -1.6 -8.8-311-9+7None of these is true.-3-18,81,62.4 3,2(1.5, -1.1)f is concave down from x = -3 to x = 0.f is decreasing from x = -1.5 to x = 1.5.f has a relative maximum at x = 1.

For the given graph of the derivative of f(x) . We have to find out which of the following is…

Answered: 25. Below is the graph of f '(x), the…

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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3.2(1) Determines the equation of the tangent to the representative curve of f(x) = 2x 2 + 4x - 1 when × = -2. (Be sure of the definition of the derivative (fundamental principles) to determine the slope of the tangent.)
If the second derivative of a function f is given byf" (x) = x (x - 1) (x + 2)“, then f has points of inflection when x =
The curve y = ax + bx +c passes through the point (1,8) and is tangent to the line y = 5x at the origin. Find a, b, and c. (Hint: You can find these numbers by doing a few things. You can plug (1,6) and the origin into y. You can find the derivative of y=f(x); what is the derivative of f(x) at the origin?
Consider the graph of f(x), the derivative of f(x). Find each of the following: You must use interval notation as needed. Use a comma to separate answers as needed. If a question has no solution, type none for the answer. y = f'(x) 4 3 2 1. f is increasing in the interval(s) 2. f is decreasing in the interval(s) -5 -4 -3 -2 -11 -2 3. f has a relative maximum at x = 5Ay 4. f is concave up in the interval(s): 11 6. f has inflection points at x = 1 -4 -5- 5. f is concave down in the interval(s): 1 2 3 4 10
3. Consider the function f(x) = r} – 5x3. 10x + 10 (a) Show that the second derivative is f"(x) (b) Find all intervals where the function f(x) is concave up or concave down.
The graph of f', the derivative of f, is shown below. Determine all possible inferences that can be made about f and f' when x = -2. y O 8 7 6 5 4 3 # 2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -N 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 /1 -7 -8 Graph of f' ·X
given that the derivative of (3x+9/(2-x)) is 15/(2-x)2 what is 5+5?
10.The graph of f'(x), the derivative of f, is given below for -6sxS7.On what intervals is the graph of the function f(x), increasing? 3 2 y = f(z) -6 -5 -4 6 Note: this is the graph of the derivative of f(x), not the graph of f(x) itself. (A) (-3,2) (B )(-3,7) (C) (-5,-1) and (5,7) (D) (-6,–3) and (2,7) (E) (-6,-5) and (-1,5)

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