5 Steps to a 5 AP Calculus BC 2019

Applications of Derivatives 163

container into the cylindrical container at

the rate of 15 ft^3 /min, how fast is the water

level falling in the conical tank when the

water level in the conical tank is 5 feet high?

How fast is the water level rising in the

cylindrical container?

17. The wall of a building has a parallel fence
    that is 6 feet high and 8 feet from the wall.
    What is the length of the shortest ladder
    that passes over the fence and leans on the
    wall? (See Figure 8.4-4.)


18. Given the cost function C(x)= 2500 +
    0. 02 x+ 0. 004 x^2 , find the product level such
    that the average cost per unit is a minimum.


19. Find the maximum area of a rectangle
    inscribed in an ellipse whose equation is
    4 x^2 + 25 y^2 =100.


20. A right triangle is in the first quadrant with
    a vertex at the origin and the other two
    vertices on thex- andy-axes. If the
    hypotenuse passes through the point
    (0.5, 4), find the vertices of the triangle so

that the length of the hypotenuse is the

shortest possible length.

Ladder

8 ft

Wall

Fence

6 ft

Figure 8.4-4

8.5 Cumulative Review Problems

(Calculator) indicates that calculators are

permitted.

21. Ify=sin^2 (cos(6x−1)), find
    dy
    dx

.

22. Evaluate limx→∞
    100 /x
    − 4 +x+x^2

.

23. The graph off′is shown in Figure 8.5-1.
    Find where the functionf: (a) has its
    relative extrema or absolute extrema; (b) is
    increasing or decreasing; (c) has its point(s)
    of inflection; (d) is concave upward or
    downward; and (e) iff(3)=−2, draw a
    possible sketch off. (See Figure 8.5-1.)

y

f′

03 x

Figure 8.5-1