(Be sure to use differential notation properly. Show all work for full credit)

1. Find and simplify the derivative.

a) $\displaystyle f(x)=4\cos{x}+x^{4/3}$

b)$\displaystyle y=\frac{1}{x}+5e^x$

2) Find the equation of the line tangent to $\displaystyle y=\cos{x}$ at $\displaystyle (\frac{4\pi}{3},-\frac{1}{2})$. Give exact coefficients and approximate coefficients to the nearest thousandth.

3) Find theaveragerate of change of $\displaystyle f(x)=x^3-\frac{4}{3}x$ on the interval $\displaystyle [-2,3]$.

4) Find theinstantaneousrate of change of w with respect to z if $\displaystyle w=\frac{7}{3z^2}$.

The answers I've got for these are:

1) a) $\displaystyle \frac{4}{3}x^{1/3}-4sinx$

b) $\displaystyle 5e^x-\frac{1}{x^2}$

2) $\displaystyle y=0.866x-3.128$

3) $\displaystyle \frac{17}{3}$

4) $\displaystyle -\frac{14}{3z^3}$

What I would like for someone to do is:

1) Tell me if my answers are correct

2) Do the problems so that I can see how you did them because I got the answers, but it wasn't pretty.

3) tell me if my answers are simplified they way they should be.

Thanks Dudes. (and dudesses)