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

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


For graph, see graphing calculator.