**Practice Exam 2**

**November 2003**

- Use
the linear approximation to estimate
_{}.

- You
are using Newton’s formula to estimate the root of x
^{3}– 3x + 1. If x_{5}= 0.2, what is x_{6}?

- Find
the absolute maximum and minimum value of the function f(x) = x
^{ 4}– 8x^{2}+1 on the interval [-1,3]. - For
the function f(x) =
_{}

give the intervals where f is increasing-decreasing, concave up-down, list the inflection points and local maxima and minima (Use either the first or second derivative test to justify your answer).

Same thing for f(x) = x^{3} – 6x^{2}
– 20x + 2.

- A farmer wishes to fence in a rectangular pasture with one side bounded by a straight river bank. He wants to divide the pasture in half with a length of fence running parallel to the river. If he has 2000 feet of fencing, what is the maximum total area he can enclose.

Other sample problems : p. 306 – 9,14,20,22

- Sketch a graph of f(x) = x/(x-1). Include the details listed by the text.

- Find
the antiderivatives: (a) 3x + 4, (b) 5sec
^{ 2}x (c) e^{-x}+ cos(x) (d) x^{-1}+ x^{-2}

- State the Mean Value Theorem. Find the point c guaranteed by the Mean Value Theorem for f(x) = 4x – 1/x on the interval [1,2]. What if the interval is [-1,1]?

- Use L’Hopital’s rule or some other rule to find the limits:

((a) _{} (b) _{}