Mathematics 150 AL

Assignment 2

Due: Feb 26, 2008

I. For the functions listed below

a) find the difference quotients

b) find the derivative using the definition of the derivative

1. $g(x)=(8x+2)^{3}$

2. $\ \ h(x)=$ $\frac{1-x}{2+x}$

3. $\ k(x)=\sqrt{x}$

Be sure to check that you get what you think you should get.

II. Compute the equation of the tangent line at the indicated point and

plot the graph of both the function and its tangent on one graph. Be sure to use an appropriate scale. (Use the same $g$, $h$, and $k$ as defined in I.)

1. $g(x);$ $\ \ \ \ \ x=0.1$

2. $\ h(x);$ $\ \ \ \ x=\ -1$

3. $k(x);$ $x=0.01$

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