# Is #f(x)=-3x^5-2x^4-6x^3+x-7# concave or convex at #x=5#?

##### 1 Answer

Aug 16, 2017

convex (concave DOWNWARD)

#### Explanation:

It's a pretty straightforward polynomial, so taking the derivative is pretty easy. You can just derive the terms one by one, proceeding left to right:

And then, do it again:

You can plug in x = 5 and calculate if you want, but if you're pressed for time on an exam it's not really necessary. Each term in the second derivative is negative for x=5, so the second derivative is therefore negative at that point, so it's convex (or concave downward) at x = 5.