What is the extreme (x+1)/(x^2-5x+6) ?

The extreme (x+1)/(x^2-5x+6) is Minimum(-1-2sqrt(3),-7+4sqrt(3)),Maximum(2sqrt(3)-1,-4sqrt(3)-7)

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extreme (x+1)/(x^2-5x+6)

extreme

Minimum (- 1 - 23, - 7 + 43), Maximum (23 - 1, - 43 - 7)

Solution steps

f^{'} (x) = \frac{- x ^{2} - 2 x + 11}{( x ^{2} - 5 x + 6 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 1 - 23,

Increasing

: - 1 - 23 < x < 2,

Increasing

: 2 < x < - 1 + 23,

Decreasing

: - 1 + 23 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1 - 23

into

\frac{x + 1}{x ^{2} - 5 x + 6} : - 7 + 43

Minimum (- 1 - 23, - 7 + 43)

Plug

x = 23 - 1

into

\frac{x + 1}{x ^{2} - 5 x + 6} : - 43 - 7

Maximum (23 - 1, - 43 - 7)

Minimum (- 1 - 23, - 7 + 43), Maximum (23 - 1, - 43 - 7)

What is the extreme (x+1)/(x^2-5x+6) ?
The extreme (x+1)/(x^2-5x+6) is Minimum(-1-2sqrt(3),-7+4sqrt(3)),Maximum(2sqrt(3)-1,-4sqrt(3)-7)