1. First Derivative Test So far…
Critical values show where potential extrema exist, but we must test the closed interval values as well.
Rolle’s Theorem, when applicable, guarantees an extrema in an open interval by using derivatives.
How can we use the derivative to prove that a critical point is a maximum or minimum?

2. First Derivative Test
Decreasing, constant and Increasing functions…

3. First Derivative Test

4. First Derivative Test

5. First Derivative Test

6. First Derivative Test

7. First Derivative Test

8. First Derivative Test
BE CAREFUL OF THE DOMAIN!!!