Question

Find the greatest and the least values of the following functions (292-296).
$f\left(x\right)=4x^2+\frac{1}{x}on[\frac{1}{4},1]$

Answer 1

$f\left(x\right)={4x}^2+\frac{1}{x}$

$f^1\left(x\right)=8x-\frac{1}{x^2}=0$ Least at $x=\frac{1}{2}$

${8x}^3-1=0$ and max at $x=1$

$x={\left(\frac{1}{8}\right)}^{1/3}$ Least value $=3$

$x=\frac{1}{2}$ greatest value $=5$