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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
