# Is #f(x)=x^4-4x^3+x-4# concave or convex at #x=-1#?

##### 1 Answer

Mar 22, 2016

convex

#### Explanation:

To find that out, we need to get the second derivative first.

**Getting the first derivative.**

*We can easily find this using power rule.*

**Getting the second derivative.**

*Use power rule again.*

**Now that we know the second derivative, we will evaluate #f''(x)# at #x=-1# to check its concavity.**

• If **concave up** or **convex**

• If **concave down** or **concave**

**Since #f(x)# is 36 at #x=-1# and 36 is greater than 0, then #f(x)# is convex at #x=-1#.**