# What are the points of inflection, if any, of f(x)=3x^5 - 5x^4 ?

Mar 22, 2016

The only inflection point is $\left(1 , - 2\right)$.

#### Explanation:

An inflection point is a point on the graph at which the inflection (concavoty) changes.

$f \left(x\right) = 3 {x}^{5} - 5 {x}^{4}$

$f ' \left(x\right) = 15 {x}^{4} - 20 {x}^{3}$

$f ' ' \left(x\right) = 60 {x}^{3} - 60 {x}^{2}$

$= 60 {x}^{2} \left(x - 1\right)$

Ths sign of $f ' '$ changes at $x = 1$, so the point $\left(1 , f \left(1\right)\right)$ is an inflection point.