Let f be the function given by f(x)= 2xe^x. determine the interval(s) on which the graph is concave down.

Using the second derivative, it is found that the graph is concave down on the interval .

A function is concave down when the second derivative is negative.

The function is:

The first derivative is as follows, applying the product rule:

The second derivative is the derivative of the first derivative, given by:

The exponential is always positive, so the second derivative is negative if:

Hence, the graph is concave down on the interval .

A similar problem is given at link

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step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

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