(4, 4) 10 12 (-4, –4) (8, –4) (12, –4) Graph of f 3. The figure above shows the graph of the piecewise-linear function f. For –45x< 12, the function g is defined by g(x) = [, 1(1) dr. (a) Does g have a relative minimum, a relative maximum, or neither at x = 10 ? Justify your answer. (b) Does the graph of g have a point of inflection at x = 4 ? Justify your answer. (c) Find the absolute minimum value and the absolute maximum value of g on the interval -4 < x< 12. Justify your answers.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 48E
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(4, 4)
10
12
-4
(-4, –4)
(8, –4)
(12,–4)
Graph of f
3. The figure above shows the graph of the piecewise-linear function f. For –4 < x < 12, the function g is defined
by g(x) = [, 1() dr.
(a) Does g have a relative minimum, a relative maximum, or neither at x = 10 ? Justify your answer.
(b) Does the graph of g have a point of inflection at x = 4 ? Justify your answer.
(c) Find the absolute minimum value and the absolute maximum value of g on the interval –4 <x < 12.
Justify your answers.
(d) For -4 < x < 12, find all intervals for which g(x) < 0.
Transcribed Image Text:(4, 4) 10 12 -4 (-4, –4) (8, –4) (12,–4) Graph of f 3. The figure above shows the graph of the piecewise-linear function f. For –4 < x < 12, the function g is defined by g(x) = [, 1() dr. (a) Does g have a relative minimum, a relative maximum, or neither at x = 10 ? Justify your answer. (b) Does the graph of g have a point of inflection at x = 4 ? Justify your answer. (c) Find the absolute minimum value and the absolute maximum value of g on the interval –4 <x < 12. Justify your answers. (d) For -4 < x < 12, find all intervals for which g(x) < 0.
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