What is the extreme f(x)=((x+4)(x+1)(x-1)(x-3))/x ?

The extreme f(x)=((x+4)(x+1)(x-1)(x-3))/x is Maximum(-2.57956…,17.37172…),Minimum(2,-9)

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extreme f(x)=((x+4)(x+1)(x-1)(x-3))/x

extreme points

f (x) = \frac{( x + 4 ) ( x + 1 ) ( x - 1 ) ( x - 3 )}{x}

Maximum (- 2.57956 \dots, 17.37172 \dots), Minimum (2, - 9)

Solution steps

Find the critical points:

x \approx - 2.57956 \dots, x = 2

Domain of

\frac{( x + 4 ) ( x + 1 ) ( x - 1 ) ( x - 3 )}{x} : x < 0 or x > 0

Find intervals:

Increasing

: - \infty < x < - 2.57956 \dots,

Decreasing

: - 2.57956 \dots < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug the extreme point

x = - 2.57956 \dots

into

\frac{( x + 4 ) ( x + 1 ) ( x - 1 ) ( x - 3 )}{x} \Rightarrow y = 17.37172 \dots

Maximum (- 2.57956 \dots, 17.37172 \dots)

Plug the extreme point

x = 2

into

\frac{( x + 4 ) ( x + 1 ) ( x - 1 ) ( x - 3 )}{x} \Rightarrow y = - 9

Minimum (2, - 9)

Maximum (- 2.57956 \dots, 17.37172 \dots), Minimum (2, - 9)

What is the extreme f(x)=((x+4)(x+1)(x-1)(x-3))/x ?
The extreme f(x)=((x+4)(x+1)(x-1)(x-3))/x is Maximum(-2.57956…,17.37172…),Minimum(2,-9)