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)
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1 answer

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. 👍
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