ruigE

2021-03-11

Let $f(x)=4-\frac{2}{x}+\frac{6}{{x}^{2}}$ .

Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

f is increasing on the intervals

f is decreasing on the intervals

The relative maxima of f occur at x =

The relative minima of f occur at x =

Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none".

In the last two, your answer should be a comma separated list of x values or the word "none".

Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

f is increasing on the intervals

f is decreasing on the intervals

The relative maxima of f occur at x =

The relative minima of f occur at x =

Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none".

In the last two, your answer should be a comma separated list of x values or the word "none".

Talisha

Skilled2021-03-12Added 93 answers

Take derivative and find out critical points to get maxima and minima

Apply power rule

Set the derivative

LCD is

multiply each term by

So

Break the numbers line into three intervals using 0 and 6

Check each interval using derivativeLet

Derivative is from positive in two intervals

So increasing intervals are

Decreasing interval

There is a break in graph of

The derivative goes from negative to positive at

So relative minima at

There is no relative maxima