Math

 Differentiate.

 Differentiate.

 Differentiate. (with respect to )

 Differentiate. (with respect to )

 Differentiate. (What will you do first to minimize computations?)

 Find an equation of the tangent line to at the point . Check your answer by graphing both the curve and the tangent line.

 Based on these graphs of and

Find: (this is the derivative of the product of and evaluated when (.) and .

 At a given time the height of a person is 5 feet and it increases at a rate of 1 inch per year. The person's weight is 100 lb and it increases at a rate of 5 lb/year. (a) What is the body fattness (BMI) of the person? (b) Is the person getting slimmer? (c) Assuming that the instantaneous rate of change of BMI does not change over a year, predict the person's BMI one year from now. Recall that the BMI index is the fraction of the body weight measured in kilograms divided by the square of the body height measure in meters.

 Use induction to show the Power Rule: for positive integers . You may proceed as follows: (a) First show that the formula is true when . (b) Then assume that it is true for some and show that it also holds for . For part (b) you may start like this and use the Product Rule:

. By following the proof that show this more general statement. Let , .