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8. 3 1 -4 -3 -2 -10 -1 -2- -3- 1 2 4 5 (3,-1) The graph of a function f consists of a semicircle and two line segments as shown above. Let g b given by g(x)=ff(t)dt. a. Find g(3). Show the work that leads to your conclusion. 2 S f ( t) d t + 5² f ( t ) d t O 9 (3) = √fft)dt = 4.2² + 1/2 (3-2)(-1²-0) ITE-_L (X-1) = ( 11 - 1/12) b. Find the values of x on the interval (-2,5) at which g has a relative maximum. Justify your a g"(x)=0 c. Write the equation of the line tangent to the graph of g at x = 3.

8. 3 1 -4 -3 -2 -10 -1 -2- -3- 1 2 4 5 (3,-1) The graph of a function f consists of a semicircle and two line segments as shown above. Let g b given by g(x)=ff(t)dt. a. Find g(3). Show the work that leads to your conclusion. 2 S f ( t) d t + 5² f ( t ) d t O 9 (3) = √fft)dt = 4.2² + 1/2 (3-2)(-1²-0) ITE-_L (X-1) = ( 11 - 1/12) b. Find the values of x on the interval (-2,5) at which g has a relative maximum. Justify your a g"(x)=0 c. Write the equation of the line tangent to the graph of g at x = 3.

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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8. y 3 1 -5 -4 -3 -2 -10 -1 -24 -3- 1 2 2 3 4 5 (3,-1) The graph of a function f consists of a semicircle and two line segments as shown above. Let g be the function given by g(x) = f* f(t)dt. a. Find g(3). Show the work that leads to your conclusion. 2 9 ( 3 ) = {f(t)dt = $²f(t)dt + 5² f ( t ) d t 0 2 4711 · 2²^² + - 1/2 (3-2) (-1-0) 17+ - 1 (x-1) = (1 - -/-/-) b. Find the values of x on the interval (-2,5) at which g has a relative maximum. Justify your answer. g" (x) = 0 c. Write the equation of the line tangent to the graph of g at x = 3.
Transcribed Image Text:8. y 3 1 -5 -4 -3 -2 -10 -1 -24 -3- 1 2 2 3 4 5 (3,-1) The graph of a function f consists of a semicircle and two line segments as shown above. Let g be the function given by g(x) = f* f(t)dt. a. Find g(3). Show the work that leads to your conclusion. 2 9 ( 3 ) = {f(t)dt = $²f(t)dt + 5² f ( t ) d t 0 2 4711 · 2²^² + - 1/2 (3-2) (-1-0) 17+ - 1 (x-1) = (1 - -/-/-) b. Find the values of x on the interval (-2,5) at which g has a relative maximum. Justify your answer. g" (x) = 0 c. Write the equation of the line tangent to the graph of g at x = 3.
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