Question

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?

2. Find the derivative of f(x) = |x + 2| at the point (1, 3)

3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15.

4. Find all values of x on the graph of f(x) = -2x3 + 15x2 - 12 at which there is a horizontal tangent line.

5. Find the equation of the tangent line to the graph of f(a) = -sec(a) at the point (0, -1)

Answer 1

I always hate to see homework dumps. I'll do a couple, but till I see some work on your part, I feel no obligation to do all your work.

#1
f(x) = cos(x)
f'(x) = -sin(x)
at the given point, f'(2) = -sin(2)

#2
Recall that
|x| = x if x >= 0
|x| = -x if x < 0
At x=1, x+1 > 0, so |x+2| = x+2
f'(x) = 1 wherever x+2 >= 0

Now do a little review and come back with some answers of your own, which we can review.