A -3 3 Graph of f The graph of a differentiable function fis shown above for -3

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 59E
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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.
Transcribed Image Text: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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