# Inflection Points and Concavity Calculator

## Find inflection points and concavity step by step

The calculator will try to find the intervals of concavity and the inflection points of the given function.

**Your input: find the inflection points and intervals of concavity of $$$f=x e^{- 5 x}$$$**

### Inflection Points

$$$\left(x, f \left(x \right)\right)=\left(\frac{2}{5},\frac{2}{5 e^{2}}\right)\approx \left(0.4,0.0541341132946451\right)$$$

### Concave upward on

$$$\left(\frac{2}{5}, \infty\right)= \left(0.4, \infty\right)$$$

### Concave downward on

$$$\left(-\infty, \frac{2}{5}\right)= \left(-\infty, 0.4\right)$$$

### Graph

For graph, see graphing calculator.