MTH 151
Quiz 4
Fall 2011

Show all work in a neat and organized fashion. Clearly indicate your answers.
20 points possible.

1. (6 pts.) Refer to the figure on the attached page, showing the graph of a function defined on [a,s]. For each of the numbers a, b, c, d, r, and s, state whether the function has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum.
2. (4 pts.) Find the differential dy of each function.

(a) y=x2cosx
(b) y=tan3x
3. (5 pts.) (a) Find the linearization L(x) of the function at a.
f(x)=√x,       a=100
(b) Use your answer to part (a) (or use differentials) to estimate the given number.

√
 
109
 
4. (5 pts.) Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV=C, where C is a constant. Suppose that at a certain instant the volume is 800 cm3, the pressure is 300 kPa, and the pressure is increasing at a rate of 25 kPa/min. At what rate is the volume changing at this instant?


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