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Use the function f plotted below to define g(x) = | f(t)dt y=f(x) -2 2 -2 Answer the following questions about the function g(x). a. Evaluate: g(0) • g(4) • g(-3) 2.

Use the function f plotted below to define g(x) = | f(t)dt y=f(x) -2 2 -2 Answer the following questions about the function g(x). a. Evaluate: g(0) • g(4) • g(-3) 2.

Advanced Engineering Mathematics
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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14 of 14 Use the function f plotted below to define g(x) = | f(t)dt 4 y=f(x) 2- 2 4 -2 Answer the following questions about the function g(x). a. Evaluate: • g(0) • g(4) • g(-3) b. Evaluate: • g'(-2) • g"(-2) c. On what interval(s) is the function g(x) concave up (you may assume the lines continue to t00)?
Transcribed Image Text:14 of 14 Use the function f plotted below to define g(x) = | f(t)dt 4 y=f(x) 2- 2 4 -2 Answer the following questions about the function g(x). a. Evaluate: • g(0) • g(4) • g(-3) b. Evaluate: • g'(-2) • g"(-2) c. On what interval(s) is the function g(x) concave up (you may assume the lines continue to t00)?
Expert Solution
Step 1

We’ll answer the first question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered.

gx=∫0xfxdx, therefore, g0=∫0ofxdx,

so g0=0

Step 2

g4=∫04fxdx: So g4 will be areas spanned by fx in from 0 to 4 i.e. area of the trapezoid: 

g4=124+4-1×2       =7

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