Question

Find all relative extrema of the function. Use the Second Derivative Test where applicable.

Answer 1

First, we will find the derivate of the function:

`\begin{gathered} f(x)=x^2+3x-8 \\ f^(\prime)(x)=2x+3 \\ f^(\prime)^(\prime)(x)=2 \end{gathered}`

Then, we will find the roots of the second derivate:

`\begin{gathered} f^(\prime)^(x)=0=2x+3 \\ 2x=-3 \\ x=-(3)/(2) \end{gathered}`

As we know, after finding the roots of the first derivative, we must replace them in the second derivative, but the second derivative has a fixed value. Since this criterion is not met, then we have no relative extrema.