What is the extreme f(x)=x^3-6x^2-9x-2 ?

The extreme f(x)=x^3-6x^2-9x-2 is Maximum(2-sqrt(7),14sqrt(7)-36),Minimum(2+sqrt(7),-36-14sqrt(7))

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extreme f(x)=x^3-6x^2-9x-2

extreme points

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

Maximum (2 - 7, 147 - 36), Minimum (2 + 7, - 36 - 147)

Solution steps

f^{'} (x) = 3 x^{2} - 12 x - 9

Find intervals:

Increasing

: - \infty < x < - 7 + 2,

Decreasing

: - 7 + 2 < x < 7 + 2,

Increasing

: 7 + 2 < x < \infty

Plug

x = 2 - 7

into

x^{3} - 6 x^{2} - 9 x - 2 : 147 - 36

Maximum (2 - 7, 147 - 36)

Plug

x = 2 + 7

into

x^{3} - 6 x^{2} - 9 x - 2 : - 36 - 147

Minimum (2 + 7, - 36 - 147)

Maximum (2 - 7, 147 - 36), Minimum (2 + 7, - 36 - 147)

f (x) = x \cdot 500 - x

f (x) = - 8 x^{2} + x^{4}

f (x) = (x^{3} - 3 x)^{\frac{1}{2}}

f (t) = 108 t - t^{3}, - 7 \leq t < \infty

f (x) = 2 ln (x) 1 + 3 ln (x) 2 + 3 ln (x) 3

What is the extreme f(x)=x^3-6x^2-9x-2 ?
The extreme f(x)=x^3-6x^2-9x-2 is Maximum(2-sqrt(7),14sqrt(7)-36),Minimum(2+sqrt(7),-36-14sqrt(7))