Differentiate and simplify your answer, leaving it in radical form and give your answer as a fraction.

1. If the position of an object moving along a straight line is given by .  at time t find its acceleration.

Answer: 

2. Differentiate  and simplify your answer, leaving it in radical form and give your answer as a fraction.

Answer: 

3. Differentiate  and simply your answer

Answer: 

4. Find the second derivative of the given function. In each cas, use the appropriate notation for the second derivative and simplify our answer. You needn’t factor your answer.

Answer:

5. Find the equation for the tangent line to the given curve at the point where x=1.

Answer: y= -29x+34

 

6. It is estimated that t years fron now, the population of a certain suburban community will be  thousand.  Derive a formula for the rate at which the populaion will be changing with respect to time t years fron now.

Answer:  thousand per year

7. It is estimated that t years fron now, the population of a certain suburban community will be  By how much will the population actually increase during the second year? During the second year, the population will increase by?

Answer: 3 thousand people.

8. Find  if it exists. Give your answer in fraction form, If it is infinite, indicate if the limit is

Answer: 

9. Do not factor the numerator of your answer. Differentiate the given function.