The graph of F consists of a semicircle and two line segments as shown (please see the attachment). Let g be the function given by:
g(x)= def.integral from 0 to x f(t)dt.
a Find g(3).
b Find all value of x on the open interval (-2,5) at which g has a relative maximum. Justify.
c Write an equation for the line tangent to the graph of g at x=3.
d Find the x coordinate of each point of inflection of the graph g on the open interval (-2,5). Justify.
A two segment graph is analyzed to find the equation of a tangent line and to calculate point values.