First, we will find the derivate of the function:
[tex]\begin{gathered} f(x)=x^2+3x-8 \\ f^{\prime}(x)=2x+3 \\ f^{\prime}^{\prime}(x)=2 \end{gathered}[/tex]
Then, we will find the roots of the second derivate:
[tex]\begin{gathered} f^{\prime}^(x)=0=2x+3 \\ 2x=-3 \\ x=-\frac{3}{2} \end{gathered}[/tex]
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.
