Assume that x and y are differentiable functions of t, Given,  Find when Type your answer in the box below.   You can use the Math equation editor to type in your answers below or you can simply type it in.    You will also show all work for this problem with answers on your answer sheet.  Failure to do both will result in no credit for this problem.

Let y = f(x) be a differentiable function for which the graph of its derivative, f/, is given below:  On what interval(s) is the graph of f decreasing?

Let y = f(x) be a differentiable function for which the graph of its derivative, f/, is given below:  On what interval(s) is the graph of f decreasing?

Suppose two integers (can be positive or negative) satisfy the conditions that the difference of the two numbers is 10 and their product is a minimum. What are the two numbers? Please type in your two answers in the box below.  Show all work for this problem on your answer sheet paper.     But, TYPE YOUR FINAL ANSWER IN THE BOX – Failure to type your answers in the box and/or failure to show all work on your answer sheet will result in no credit for this question.

A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute.  How fast is the radius of the balloon increasing at the instant the radius is 30 centimeters?   Type your rate of change below. You can use the Math equation editor to type in your answers below or you can simply type it in.    You will also show all work for this problem with answers on your answer sheet.  Failure to do both will result in no credit for this problem.

Suppose two integers (can be positive or negative) satisfy the conditions that the difference of the two numbers is 14 and their product is a minimum. What are the two numbers? Please type in your two answers in the box below.  Show all work for this problem on your answer sheet paper.     But, TYPE YOUR FINAL ANSWER IN THE BOX – Failure to type your answers in the box and/or failure to show all work on your answer sheet will result in no credit for this question.

Sketch the graph and show all extrema, inflection points, and asymptotes where applicable.  Be sure to select the correct answer below.   Select the correct answer below.  You will also show all work for this problem with answers on your answer sheet.  Failure to do both will result in no credit for this problem. f(x) =

Bonus Question — worth 3 points  — Type your final answer below.  You will also show all work for this problem with answers on your answer sheet.  Failure to do both will result in no credit for this problem.You must show all steps to receive any bonus credit. Given

Use the first derivative to fill in the blanks below. Write N/A if not applicable to this problem.  Show all work on your scratch paper.    

  Find the absolute maximum value and absolute minimum value of each function on the indicated interval.