# 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.

Enter a function of one variable:
Enter an interval:
Required only for trigonometric functions. For example, [0, 2pi] or (-pi, oo). If you need oo, type inf.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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.