C-3-2-1 B0123Graph of fThe graph of a differentiable function fis shown above for -3

(a)To find all the values of x on -3<x<3 for which the function g has relative maximum: From…

Answered: A -3 3 Graph of f The graph of a…

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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C
-3
-2
-1 B0
1
2
3
Graph of f
The graph of a differentiable function fis shown above for -3<x5 3. The graph of fhas
horizontal tangent lines at x = -1, x =1, and x = 2. The areas of regions A, B, C, and D are 5, 4,
5, and 3, respectively. Let g be the antiderivative of f such that g(3) = 7.
(a) Find all values of x on the open interval -3<x< 3 for which the functiong has a relative
maximum. Justify your answer.
(b) On what open intervals contained in -3<x<3 is the graph of g concave up? Give a
reason for your answer.
g(x) +1
(c) Find the value of lim-
2.r
or state that it does not exist. Show the work that leads to
your answer.
(d) Let h be the function defined by h(x) = 3f(2x +1) +4. Find the value of h(x) dx.

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But the area under a curve is not positive if it's below the x-axis. Area can be negative when it is under the x-axis. Area is routinely negative when we find the area under a cure using integrals. Why would you say that the area cannot be negative?

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Why isn't region B -4 instead of positive 4?

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