Question

8. Consider the function f whose graph consists of four line segments and a semicircle as shown below. Define g(x) by g(x) = 5 f(t)dt. Note: The graph is of the function f. The graph of g is NOT shown to you. a) Find all values of x with –5 < x < 5 for which g'(x) = 0. Explain your reasoning. b) Find g(-1) and g"(-1). Show the work that leads to your answers. c) Find all values of x with –5 < x < 5 for which g is both increasing and concave up. Justify your answer. d) What is the maximum value of g on the interval –5 < x < 5? Show the work that leads to your answer.

Answer 1

I wait can biven, gou- & fuldt :-55x5 othis impliest glx = f(x) Now, gral=0 implies fox=0 -59-39-17195 gilla I fehlt -- (6) area of the triangle with bax & and height a. 5x2x2=2 g" G1=f60 a slope of the live passing through 2, 27 and Coggy (0 - ge g u increasing and concate up implies- logoo and gloro a foulso and fouro from the graph - XE (398) U (193) (d) Maximum value of a will occur either at suitical bouts of g a at the end poests of interval [55]

Date ID At cuttical points gloxo exa-59-3,72195 Nawa ge-5) = q fedt 11982=1X2XL+ 4x2x2 1965)= g Similaslya 96375 14912454942 0 1963)=0 g610=42 XX = 12 Igozo 9657 = Area of semicekele. g(5) = b (g) ² - [T] ". Maxinum Value of g is 197.