What is the extreme x^3-3x^2-9x+1 ?

The extreme x^3-3x^2-9x+1 is Maximum(-1,6),Minimum(3,-26)

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extreme x^3-3x^2-9x+1

extreme points

x^{3} - 3 x^{2} - 9 x + 1

Maximum (- 1, 6), Minimum (3, - 26)

Solution steps

f^{'} (x) = 3 x^{2} - 6 x - 9

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 1

into

x^{3} - 3 x^{2} - 9 x + 1 : 6

Maximum (- 1, 6)

Plug

x = 3

into

x^{3} - 3 x^{2} - 9 x + 1 : - 26

Minimum (3, - 26)

Maximum (- 1, 6), Minimum (3, - 26)

f (x) = x^{2} + x y + y^{2} - 2 x + 2 y - 8

f (x) = x^{2} - y^{2} - 2 x + 4 y + 6

f (x) = 2 x^{3} - 9 x^{2} + 12 x + 6, 0 \leq x \leq 3

y = \frac{x}{x ^{2} - x + 4}

\frac{4 x}{1 + 9 x ^{2}}

What is the extreme x^3-3x^2-9x+1 ?
The extreme x^3-3x^2-9x+1 is Maximum(-1,6),Minimum(3,-26)