Download 4 REVIEW 4

AP CALCULUS - REVIEW 4.6
1. Find the absolute minimum value of the function f (x) = 2x 2 − 6x + 5 .
2. Find the area of the largest rectangle with lower base on the x-axis
and upper vertices on the parabola y = 6 − x 2
3. A particle moves along the curve y = x 2 + 4 x + 2 in such a way that the x-coordinate increases
at a steady rate of 10m/s. Find the change in the y-coordinate when x = 2.
4. A rectangular field is to be bounded by a fence on three sides and a river of the fourth. Find
the dimensions of the field with maximum area that can be enclosed with 100 ft. of fence.
5. A ladder 17 ft. long leans against a vertical wall. The top of the ladder slides down the wall at
5 ft./s. At what rate is the foot of the ladder moving away from the wall when the top of the
ladder is 15 ft. from the ground?
6. The radius of a circle is increasing at the rate of 4 cm/s. At what rate is the area of the circle
increasing when the radius is 10 cm?
7. The length of a rectangle is decreasing at the rate of 2 cm/s and the width is increasing at the
rate of 4 cm/s. When the width is 9 cm and the length is 12 cm, find the rate of change of the
area.
8. The sum of two positive numbers is 12. Find the numbers if the product of one of the numbers
and the square of the other is a maximum.
9. Water is withdrawn from a conical reservoir whose height and radius are always equal. If the
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radius decreases at 2 ft/min, at what rate is the volume ( V = π r 2 h ) of the reservoir
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decreasing when the radius is 8 ft?
10. An open box (no top) with a square base and rectangular sides is to hold 8 cu. ft. If the sides
cost $1.00 per square foot and the base costs $2.00 per square foot, find the cost of the least
expensive box.