# On what interval is f concave upward? f(x)=xln(x)

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#f(x)=xln(x)# is concave up when #f''(x)>0#

##### 1 Answer

#### Explanation:

To start off, we must realize that a function

To find

Product Rule (Simplified format of the rule): (Derivative of first)(Second function) + (First function)(Derivative of the second function)

Derivative of the natural logarithmic function:

Now we need to take the derivative of this in order to find

Remember that this question is asking us to look for when the function is concave up, meaning where

Since

The final answer is that the function