Prof. A. Suciu Name:

MTH 1733  QUIZ 2  Fall 1997

1. Sketch the curve y = x^{3} + \frac{3}{2}x^{2} − 6x + 4, indicating all relative extreme points and inflection points.

2. Use derivatives to estimate the value of \sqrt[3]{27.5}. Compare the answer to the calculator answer—to how many decimals do the two answers agree?

MTH 1733  Quiz 2  Fall 1997

3. For each of the following curves, determine the equations of the asymptotes, if any:

(a) y = \frac{x − 1}{x^{2} − 9}

(b) y = \frac{2x + 2}{3x − 4}

(c) y = \frac{x^{3} + 2}{x^{2} + 4}

(d) y = \frac{3}{\sqrt{x}} + \frac{x}{2} − 5

4. Differentiate the following functions:

(a) f(x) = (x^{3} + x^{− \frac{2}{5}} )(x^{2} − x^{\frac{2}{5}} )

(b) f(x) = ((x^{2} + 1)^{3} + 1)^{4}

(c) f(x) = \frac{\frac{1}{x} − x}{\frac{1}{x} + x}