1. Consider the function

a) Find *f*'(*x*).

b) Find the slope of the line tangent to the curve *y*=*f*(*x*)
at
*x*=0.

c) Find the equation of this tangent line.

d) Use this tangent line to approximate *f*(0.01).

2. From the following table, estimate *f*'(1). Indicate clearly
how you obtain your answer:

3. Evaluate the following limits, if they exist (or write DNE if they do not).

a)

b)

c)

d)

4. Take the derivatives of the following functions with respect to *x*.
You do not need to simplify your answers:

a)

b)

c)

d)

5. New England Widget Technologies (NEWT) makes expensive high-tech
widgets. Their marketing department has determined that the demand function
is *x* = 4000 - 2*p*, where *x* is the number of widgets
sold and *p* is the price. Their cost function is *C*(*x*)=
200,000 + 1000*x*.

a) Find the price *p*(*x*) and the revenue *R*(*x*)
as a function of *x*.

b) Compute the marginal cost, marginal revenue and marginal profit as
a function of *x*.

c) The company has a current production level of *x*=1500. To increase
*revenue*, should the company increase or decrease production? [Note:
you do *not* need to compute the optimal level of production. You
just need to say whether it is higher or lower than 1500.]

c) The company has a current production level of *x*=1500. To increase
*profit*, should the company increase or decrease production?