Sketch the graph of a function y = f(x) that satisfies all of the following characteristics. Be sure to note any places where the function is not differentiable.
• f'(x) < 0 for −1 < x < 4
• f'(x) > 0 for x < −1 and 4 < x
• f''(x) < 0 for x < −2 and 4 < x
• f''(x) > 0 for −2 < x < 4

Determine the relationship of ab and cd given the following points

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

If you flip a coin 3 times, what is the probability of flipping heads 3 times? a. p(3 heads) = 3/8 b. p(3 heads) = 1/6 c. p(3 heads) = 1/8 d. p(3 heads) = 1/2