Let f(x) = -sin(x). Based on the discussion in this section, what is a reasonable formula for f'(x)?
Look at the graph of f(x) = -sin(x).
The graph of -sin x looks like this:
We can see its derivative will be 0 at and :
And from the discussion earlier, the largest its slope will be is 1 and the smallest is -1. We can see from the picture where these largest and smallest slopes happen:
This lets us plot some points for the derivative function:
and if we connect the dots in a nice smooth curve, we find the graph of -cos x: