The graph of the continuous function f, consisting of three line segments and a semicircle, is shown above. Let g be the function given by 8(x) = , f(t) dr. (a) Find g(-6) and g(3). (b) Find g'(0). (c) Find all values of x on the open interval -6

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 36E
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The graph of the continuous function f, consisting of three line segments
and a semicircle, is shown above. Let g be the function given by
g(x) = f₁ (1) di.
(a) Find g(-6) and g(3).
(b) Find g(0).
(c) Find all values of x on the open interval -6<x<3 for which the
graph of g has a horizontal tangent. Determine whether g has a
local maximum, a local minimum, or neither at each of these values.
Justify your answers.
6
(-4,5)
4
M
-6
-4
4
(3.-21
Graph of F
(d) Find all values of x on the open interval -6<x<3 for which the graph of g has a point of inflection.
Explain your reasoning.
Transcribed Image Text:The graph of the continuous function f, consisting of three line segments and a semicircle, is shown above. Let g be the function given by g(x) = f₁ (1) di. (a) Find g(-6) and g(3). (b) Find g(0). (c) Find all values of x on the open interval -6<x<3 for which the graph of g has a horizontal tangent. Determine whether g has a local maximum, a local minimum, or neither at each of these values. Justify your answers. 6 (-4,5) 4 M -6 -4 4 (3.-21 Graph of F (d) Find all values of x on the open interval -6<x<3 for which the graph of g has a point of inflection. Explain your reasoning.
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