The temperature in an industrial pasteurization tank isf(x) =x²9x+119

degrees centigrade afterxminutes (for0x14).

(a)

Findf'(x)

by using the definition of the derivative.

f'(x) =

(b)

Use your answer to part (a) to find the instantaneous rate of change of the temperature after3minutes. Be sure to interpret the sign of your answer.

The temperature is

---Select---

increasing

decreasing

at a rate ofdegrees per minute after3minutes.

(c)

Use your answer to part (a) to find the instantaneous rate of change after8minutes.

The temperature is

---Select---

increasing

decreasing

at a rate ofdegrees per minute after8minutes.