The figure below shows the graph of f ', the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4.

Question

The figure below shows the graph of f ', the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4.

Find the x-value where f attains its absolute minimum value on the closed interval from x = -2 to x = 6. Justify your answer

Answer 1

f(x0 has lcal extrima: local maximum at (2,0) and local minimum at (4, -2.5), but absolute extrima f(x) riches at end points of interval [- 2, 6]. Absolute minimum -3 at end point -2 of given interval.