1)

Given

*f*(1) = 0, and

*f '*(1) = 8, evaluate

Limits as it results to

, so differentiate top and bottom using Chain Rule:

2) If

*f*(2) = 13 and

*f '*(

*x*) ≥ 1 for 4 ≤

*x* ≤ 4, how small can

*f*(4) possibly be?

f(4) - f(2) = f'(c)(4-2)

f(4) = 13 + (2)f'(c) > 1

?

The last step, and where to go from there is what I'm a little shaky on.

3)

where q = hx

h and c are both constants, to my knowledge.

We were taught to do this in a way that seems a little convoluted, but here's as far as I got with this one:

=

From that point we can just take the limit of e to the g'(x), so

=

Then I get stuck again, because the derivative of the bottom is

I'm imaging there has to be a way to simplify that, but I can't think of it.