1. The temperature in an industrial pasteurization tank is () = ^2 8 + 112 degrees centigrade after x minutes (for 0 12). a) Find () by using the limit definition of a derivative.

b) Use your answer to part a) to find the instantaneous rate of change of the temperature after 4 minutes. Be sure to interpret the sign of your answer.

2. After making a sign diagram for the derivative of the rational function () = x^2+4/x^2-4 find all relative

extreme points and any asymptotes if they exist.

3. For the equation, use implicit differentiation to find dy/dx and evaluate it at the given numbers.

^2 + ^2 = + 7 at = 3, = 2.