Problem Name

Problem Description

Notes

derivative_61

Find formulas for the derivative and the second derivative, and determine the value of corresponding to maximum or minimum points and say which it is.

derivative_62

The second derivative of a position function is known in physics as the acceleration. Find the acceleration of Sam's beach ball when he tosses it straight up into the air (). Is the acceleration positive or negative?

derivative_63

The second derivative of a position function is known in physics as the acceleration. Find the acceleration of a ball when Sam throws it off Mingus Mountain ().

derivative_64

The second derivative of a position function is known in physics as the acceleration. Find the acceleration of Mary when she slides on Ice Skating Lake ().

derivative_65

Consider the curve on the interval to . Find the absolute maximum value obtained by on this interval. Find the absolute minimum value obtained by on this interval.

derivative_66

Consider the curve .
a. What are the coordinates of the points where the curve has horizontal tangents?
b. How many such points are there?
c. Are these points local maximum points or local minimum points?
d. In what interval is the curve concave downward?
e. When is it concave upward?

derivative_67

Consider the curve .
a. Where is the curve rising?
b. Where is it falling?
c. Where is it concave upward?
d. Where is it concave downward?

derivative_68

If , what?

derivative_69

If , what?

derivative_70

If , what?