Problem 52

Step 1.

Using a second derivative of function we can conclude if function is concave upward or downward. Let's find the second derivative of the function 

 

                          Use The Product Rule  

              Use The Power Rule  

                               Simplify. 

Find derivative of obtained function. That will be second derivative of function .

\begin{array}{rlr}

                      Use The Product Rule

            Use The Power Rule

             Simplify.

 

Recall that the function is concave downward if

$$

\begin{aligned}

&  

 

Solving quadratic inequality we obtain interval: