Let f be the continuous function defined on [-4, 3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) = f(t) dt. (a) Find the values of g(2) and g(-2). (b) For each of g'(-3) and g"(-3), find the value or state that it does not exist. (-4,1)✔ (-2, 3) (1, 0) (3,-1) (c) Find the x-coordinate of each point at which the graph of g has a horizontal tangent line. For each Graph of f of these points, determine whether g has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers. (d) For -4 < x < 3, find all values of x for which the graph of g has a point of inflection. Explain your reasoning.
Let f be the continuous function defined on [-4, 3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) = f(t) dt. (a) Find the values of g(2) and g(-2). (b) For each of g'(-3) and g"(-3), find the value or state that it does not exist. (-4,1)✔ (-2, 3) (1, 0) (3,-1) (c) Find the x-coordinate of each point at which the graph of g has a horizontal tangent line. For each Graph of f of these points, determine whether g has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers. (d) For -4 < x < 3, find all values of x for which the graph of g has a point of inflection. Explain your reasoning.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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