Do parts (a), (c), and (d) of the following AP problem. Skip part (b). Note: You

Question

Do parts (a), (c), and (d) of the following AP problem. Skip part (b). Note: You may ignore the information about the areas of the regions bounded by the graph of f' and the x -axis. The figure above shows the graph of f, the derivative of a twice-differentiable function f,on the closed interval Os x s 8. The graph of f' has horizontal tangent lines at x = 1, x 3, and x-5. The areas of the regions between the graph of f and the x-axis are labeled in theea 2 figure. The function f is defined for all real numbers and as satisfies f(8) = 4. (8.5) 3,4) Area 7 Area Area 3 Find all values of x on the open interval 0

Explanation / Answer

a) The function has a local minimum at two values of x. x=2 and x=5 as local minimum is defined as the point which has a smaller value compared to its immediate neighborhood.

b) Absolute minimum value of f is -2.

c) In the region with area 6 and in the region with area 7 as the double derivative of f is negative.

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