# Second Derivative Test

![image](https://user-images.githubusercontent.com/14041622/40632918-6eb231ba-631e-11e8-89f6-68f3c347ac24.png)

## Example

![image](https://user-images.githubusercontent.com/14041622/40633285-589b4a8a-6321-11e8-8d8d-f0564c51e91d.png) Solve:

* `f'(c) = 0` means `c` is a critical point, could be max, min, inflection.
* `f''(c) < 0` means around point `c` it's a Downward Concave.
* Conclusion then is that `c` is a maximum point.

## Example

![image](https://user-images.githubusercontent.com/14041622/40633351-c39c421c-6321-11e8-8e23-0137876de182.png) Solve:

* `f'(c) = 0` means `c` is a critical point, could be max, min, inflection.
* `f''(c) = 0` means it's either a Concave up or down, we don't know yet.
* So the answer is "No enough information to tell."

## Example

![image](https://user-images.githubusercontent.com/14041622/40635208-81c09776-632b-11e8-8e16-b1ba89b6bf54.png) Solve:

* It's Concave Down when `f''(x) < 0`
* Find formula of `f''(x)` and set inequality equation `f''(x)<0` and solve to get `x > 2`.