MTH 1733 -- Honors Calculus 1 -- Fall 1997

Quiz 2

Sketch the curve $\displaystyle{y=x^3+\frac{3}{2} x^2-6x+4}$ , indicating all relative extreme points and inflection points.
Use derivatives to estimate the value of $\displaystyle{\root{3}\of{27.5}}$ . Compare the answer to the calculator answer--to how many decimals do the two answers agree?
For each of the following curves, determine the equations of the asymptotes, if any:
- $\displaystyle{y=\frac{x-1}{x^2-9}}$
- $\displaystyle{y=\frac{2x+2}{3x-4}}$
- $\displaystyle{y=\frac{x^3+2}{x^2+4}}$
- $\displaystyle{y=\frac{3}{\sqrt{x}}+\frac{x}{2}-5}$
Differentiate the following functions:
- $\displaystyle{f(x)=(x^3+x^{-\frac{2}{5}})(x^2-x^{\frac{2}{5}})}$
- $\displaystyle{f(x)=((x^2+1)^3+1)^4}$
- $\displaystyle{f(x)=\frac{\displaystyle{\frac{1}{x}}-x}{\displaystyle{\frac{1}{x}}+x}}$

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Created by Alexandru Suciu, Mon Oct 20, 1997

http://www.math.neu.edu/~suciu/mth1733/1733f97.q2/index.html