Question

PLEASE HELPPPP!

Consider the function f(x) = 4x+2x^-1. For this function there are four important intervals: (-\infty, A], [A,B),(B,C), and [C,\infty) where A, and C are the critical numbers and the function is not defined at B.
Find A,B,C
Tell whether the interval is increasing or decreasing

Answer 1

sorry your screwed I have no idea.

Answer 2

good thing there are other people who use this site

Answer 3

@SolomonZelman can you please help me with the question?

Answer 4

Idk how to do this prob

Answer 5

\[f(x)=4x+2x^{-1}~~\Rightarrow~~f'(x)=4-2x^{-2}=4-\frac{2}{x^2}\]
Critical points (note first that \(x=0\) is a critical point since \(f'(x)\) is undefined here):
\[\begin{align*}
4-\frac{2}{x^2}&=0\\
4&=\frac{2}{x^2}\\
2x^2-1&=0\\\\
x^2-\frac{1}{2}&=0\\\\
x&=\pm\frac{1}{\sqrt2}
\end{align*}\]
So the intervals would be
\[\left(-\infty,-\frac{1}{\sqrt2}\right)\\
\left(-\frac{1}{\sqrt2},0\right)\\
\left(0,\frac{1}{\sqrt2}\right)\\
\left(\frac{1}{\sqrt2},\infty\right)\]

Answer 6

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