What is the extreme f(x)=-2x^3+33x^2-108x+1 ?

The extreme f(x)=-2x^3+33x^2-108x+1 is Minimum(2,-99),Maximum(9,244)

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extreme f(x)=-2x^3+33x^2-108x+1

extreme points

f (x) = - 2 x^{3} + 33 x^{2} - 108 x + 1

Minimum (2, - 99), Maximum (9, 244)

Solution steps

f^{'} (x) = - 6 x^{2} + 66 x - 108

Find intervals:

Decreasing

: - \infty < x < 2,

Increasing

: 2 < x < 9,

Decreasing

: 9 < x < \infty

Plug

x = 2

into

- 2 x^{3} + 33 x^{2} - 108 x + 1 : - 99

Minimum (2, - 99)

Plug

x = 9

into

- 2 x^{3} + 33 x^{2} - 108 x + 1 : 244

Maximum (9, 244)

Minimum (2, - 99), Maximum (9, 244)

f (x) = 5 x^{2} x + 1

f (x) = 3 cos^{2} (x), 0 \leq x \leq π

f (x) = - 8 x^{\frac{6}{5}} + 4 x^{\frac{2}{5}}

f (x, y) = x^{2} + 3 x y + y^{2}

f (x) = 4 - (x - 5)^{5}

What is the extreme f(x)=-2x^3+33x^2-108x+1 ?
The extreme f(x)=-2x^3+33x^2-108x+1 is Minimum(2,-99),Maximum(9,244)