What is the extreme f(x)=-x^3+6x^2-9x-1 ?

The extreme f(x)=-x^3+6x^2-9x-1 is Minimum(1,-5),Maximum(3,-1)

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extreme f(x)=-x^3+6x^2-9x-1

extreme points

f (x) = - x^{3} + 6 x^{2} - 9 x - 1

Minimum (1, - 5), Maximum (3, - 1)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 1

into

- x^{3} + 6 x^{2} - 9 x - 1 : - 5

Minimum (1, - 5)

Plug

x = 3

into

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

Maximum (3, - 1)

Minimum (1, - 5), Maximum (3, - 1)

f (x) = (- \frac{1}{100} (x) (x - 300))

f (x) = 2 x + 6, - 4 \leq x \leq 2

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

f (x) = 1 - x^{\frac{4}{5}}

f (x) = 4 + 5 x + x^{2}

What is the extreme f(x)=-x^3+6x^2-9x-1 ?
The extreme f(x)=-x^3+6x^2-9x-1 is Minimum(1,-5),Maximum(3,-1)