Find the exact location of all the relative and absolute maxima of the function. $f ( x ) = \frac { 8 } { x } - \frac { 4 } { x ^ { 2 } }$
Select all correct answers.

A) $( 1 , - 4 )$ - absolute maximum
B) $( 4 , - 8 )$ - absolute minimum
C) $( - 1,8 )$ - relative maximum
D) $( 1,4 )$ - absolute minimum
E) $( 1,4 )$ - absolute maximum

Question

Find the exact location of all the relative and absolute maxima of the function.   $f ( x ) = \frac { 8 } { x } - \frac { 4 } { x ^ { 2 } }$ 
Select all correct answers.
 
A) $( 1 , - 4 )$ - absolute maximum
B) $( 4 , - 8 )$ - absolute minimum
C) $( - 1,8 )$ - relative maximum
D) $( 1,4 )$ - absolute minimum
E) $( 1,4 )$ - absolute maximum

Quizplus · Accepted Answer

To find the maxima and minima of $f(x) = \frac{8}{x} - \frac{4}{x^2}$, we first find its derivative: $f'(x) = -\frac{8}{x^2} + \frac{8}{x^3}$. Setting $f'(x) = 0$ gives $x = 1$. Evaluating $f(1) = 4$ shows an absolute maximum at $(1, 4)$ since the function decreases on either side of $x = 1$ and has no other critical points in its domain.

Find the Exact Location of All the Relative and Absolute f(x)=8x−4x2f ( x ) = \frac { 8 } { x } - \frac { 4 } { x ^ { 2 } }f(x)=x8​−x24​

Find the Exact Location of All the Relative and Absolute $f ( x ) = \frac { 8 } { x } - \frac { 4 } { x ^ { 2 } }$