Exam 3: Shortcuts to Differentiation

Find the derivative of .

The following table gives values for two functions f and g and their derivatives. What is ? Round to 2 decimal places.

If , find

The population of Mexico in millions is described by the formula , where t is the number of years after 1980. In the year 2025, the population will be increasing at the rate of _____ million people per year. Round to 2 decimal places.

The first derivative of is .

A landlord rents an apartment building with 250 apartments. The monthly profit, in dollars, can be modeled by , where x is the number of apartments rented. How many apartments should be rented to maximize profit?

Find the first derivative of .

Differentiating gives .

The population of Mexico in millions is described by the formula , where t is the number of years after 1980. How many years will it take for the population to triple? Round to 2 decimal places.

The first derivative of is .

Find the first derivative of .

A drug's concentration is modeled by with C in mg/ml and t in minutes. Is C'(t) positive or negative when t = 35 ? Find and interpret C'(35) in terms of drug concentration

The first derivative of is .

The first derivative of is .

Find the first derivative of .

Find the equation of the line tangent to at , (A) using exact values and (B) to three decimal places.

What is the equation of the tangent line to at the point where x = 1?

Find the derivative of .

Differentiate .

A. The equation for the tangent line to the curve when x = 4 is y = _____x + _____. B. The tangent line meets the y-axis at y = _____ and the x-axis at x = _____.