Let f(x)be a function with positive values and let $g=\sqrt{f}$ .If f has a local maximum at $x=x_{0}$ , what about g?
A)g has a local maximum at $x=x_{0}$
B)g has a local minimum at $x=x_{0}$
C)g could have a local maximum or a local minimum at $x=x_{0}$

Question

Quizplus · Accepted Answer

Since $f(x)$ has a local maximum at $x=x_{0}$, $f(x)$ is decreasing on both sides of $x_{0}$. The square root function $g=\sqrt{f}$ is monotonically increasing, meaning if $f(x)$ decreases, $g(x)$ also decreases but at a slower rate. Thus, $g(x)$ will also have a local maximum at $x=x_{0}$.

Let F(x)be a Function with Positive Values and Let g=fg=\sqrt{f}g=f​ If F Has a Local Maximum At and Let

Let F(x)be a Function with Positive Values and Let $g=\sqrt{f}$ If F Has a Local Maximum At and Let