2. Where a function increases or decreases can be determined by plugging numbers greater than and less than the critical point (possible maximums or minimums) into f'. Where these values are positive, the function is increasing; where these values are negative, the function is decreasing.
3. The chain rule is a process for finding the derivative of a composite function. This is done by taking the derivative of the outside function, rewriting the inside function, and multiplying by the derivative of the inside function.
Example:
tangent line at x=1
4. h(x)=f(g(x))
g(-4)=5, g'(-4)=2, f'(5)=20 find h'(-4)
h'(x)=f'(g(x))g'(x)
h'(-4)=f'(g(-4))g'(-4)
h'(-4)=f'(5)2
h'(-4)=20(2)
h'(-4)=40
