Inflection Points and Concavity Calculator

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.

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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.