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This is a calculus 1 quiz about related rates and critical values. Please write the complete detail and process of how to solve these 5 questions. The quiz is in the attachment. thanks.
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Math 220 (Take home) Quiz 5
This quiz contains problems as seen in Sections 12 through 15. You are only allowed to use your
book, notes, and the instructor as resources. You are not allowed to work with other
students. Please show all work. Problems without work will receive no credit. Problems are to
be done on a separate piece of paper to be handed in at the beginning of class. Your assignment
must be clean, neat, stapled, and without “frills” on the end of the paper. You will lose credit if
your work does not follow these rules! Due Wednesday, March 6th.
1. An object’s height in meters at time t seconds is given by s(t) = −4t3 + 18t2 − 15t + 9.
Determine the object’s acceleration at 2 seconds. Include appropriate units in your answer.
(1 points)
2. A company’s cost (in dollars) for producing q items is given by C = 12500 + 8q − .002q 2 .
What is the approximate cost for the company to produce the 51st item? Include
appropriate units and do not use a calculator. (2 points)
dy
3. Use implicit differentiation to find dx
for the equation 2x3 y 2 − 10xy = 12x. Then determine
the equation of the line tangent to the curve at (1, −1) in slope-intercept form. Please
simplify all fractions. (2 points)
4. A rectangle’s length is increasing at a rate of 4 meters per minute and its width is
decreasing at a rate of 2 meters per minute. How is the area of the rectangle changing when
its length is 5 meters and its width is 3 meters? Is the area increasing or decreasing?
Include appropriate units in your answer. (3 points)
5. Find the critical numbers of f (x) = 14 x4 − 35 x3 + 3x2 . (2 points)
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