Find the x-axis Find the x-value of all points where the function below has any relative extrema....

Question:

Find the x-axis Find the x-value of all points where the function below has any relative extrema. Find the value(s) of any relative extrema.

{eq}f\left ( x \right ) = x^2 + 5x + 2 {/eq}

Relative Extrema:

The points of the function where the function have a relative maximum or relative minimum are called relative extrema of the function.

These points are found at the solutions to the equation {eq}\displaystyle f'(x)=0 {/eq}.

Formula Used For Differentiation:

{eq}\displaystyle (x^n)'=nx^{n-1} {/eq}.

Answer and Explanation:

Given function {eq}\displaystyle f(x)=x^2+5x+2 {/eq}.

Differentiating the function with respect to {eq}\displaystyle x {/eq}.

{eq}\displaystyle f'(x)=2x+5 {/eq}.

Points of extrema are given by:

{eq}\displaystyle \begin{align} f'(x)&=0\\ 2x+5&=0\\ x&=\frac{-5}{2}. \end{align} {/eq}

The function has a relative extrema at {eq}\displaystyle x=\frac{-5}{2}. {/eq}


Learn more about this topic:

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How to Determine Maximum and Minimum Values of a Graph

from Math 104: Calculus

Chapter 10 / Lesson 3
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