2. Consider a function f that consists of the four line segments joining the points (0,0), (2, -3), (4,5), (6,2) and (8,-2). The function F is defined by the integral F(x) = f(t), dt = [₁ (a) Sketch the graph of f. (b) From your graph and simple geometric formulas, complete the table: 012345678 x F(x) (c) Find the critical numbers for F, the intervals where F is increasing or decreasing, and find all extrema of F on the interval [0,8]. (d) Determine the intervals where F is concave up or concave down, and find all points of inflection of F on the interval (0,8).
2. Consider a function f that consists of the four line segments joining the points (0,0), (2, -3), (4,5), (6,2) and (8,-2). The function F is defined by the integral F(x) = f(t), dt = [₁ (a) Sketch the graph of f. (b) From your graph and simple geometric formulas, complete the table: 012345678 x F(x) (c) Find the critical numbers for F, the intervals where F is increasing or decreasing, and find all extrema of F on the interval [0,8]. (d) Determine the intervals where F is concave up or concave down, and find all points of inflection of F on the interval (0,8).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 41E
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![2. Consider a function f that consists of the four line segments joining the points (0,0), (2, -3), (4,5), (6,2)
and (8,-2). The function F is defined by the integral
F(x) = [ f(t),dt
(a) Sketch the graph of f.
(b) From your graph and simple geometric formulas, complete the table:
x 0 1 2 3 4 5 6 7 8
F(x)
(c) Find the critical numbers for F, the intervals where F is increasing or decreasing, and find all
extrema of F on the interval [0,8].
(d) Determine the intervals where F is concave up or concave down, and find all points of inflection of
F on the interval (0,8).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabe6e386-5af5-4a0c-9d83-519a01380f7e%2F98146739-7762-4bbe-9f84-53e735ddf94b%2Fopge2ce_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider a function f that consists of the four line segments joining the points (0,0), (2, -3), (4,5), (6,2)
and (8,-2). The function F is defined by the integral
F(x) = [ f(t),dt
(a) Sketch the graph of f.
(b) From your graph and simple geometric formulas, complete the table:
x 0 1 2 3 4 5 6 7 8
F(x)
(c) Find the critical numbers for F, the intervals where F is increasing or decreasing, and find all
extrema of F on the interval [0,8].
(d) Determine the intervals where F is concave up or concave down, and find all points of inflection of
F on the interval (0,8).
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