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Two Segment Graph : Equation of Tangent and Calculation of Points

Please note: On the attached graph the scale is that each line represents one unit. Please show all work, thanks!!

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.


Solution Summary

A two segment graph is analyzed to find the equation of a tangent line and to calculate point values.