115 PRACTICE MIDTERM II
Please work out each of the given problems.
Credit will be based on the steps that you show towards the final answer.
Show your work.
PROBLEM 1 Find
for the following
1 - x2
B) y = (2 - 3x)14
y = x2 sin(x - x4 )
3x2 - x2y + y4
A zoo keeper plans to build a rectangular cage for
her newly arrived panda bears. The
front of the cage is to be made of glass at a cost of $100
per foot and the other three sides of the cage are to be made of concrete
costing $50 per foot.
If the zoo keeper has $3000 to spend on the
cage, what dimensions should the cage be so as to maximize the area of the cage?
The nearby sewage plant has just announced that it had a chlorine gas spill. The gas cloud is in the shape of a hemisphere with equator on the ground. The volume of the cloud is expanding at a rate of 10,000 cubic feet per minute. How fast is the radius of the cloud moving by the time the cloud has reached the campus gym which is 200 feet away? (Hint: the volume of a hemisphere is
and you want to find out how fast the radius is changing.)
Without the use of the graphing capability of a graphing calculator, use calculus to find where the following function is increasing and decreasing. Also use the first derivative test to locate and classify the relative extrema.
y = 2x3 - 3x2
The profit made is selling x automobiles can be modeled by the equation
P = x2(8x2 + x) -1/2
Find the marginal profit when x = 1.
y = x3 - 12x
on the closed interval [0,3].Solution