What is the extreme f(x)=2+54x-2x^3 ?

The extreme f(x)=2+54x-2x^3 is Minimum(-3,-106),Maximum(3,110)

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extreme f(x)=2+54x-2x^3

extreme points

f (x) = 2 + 54 x - 2 x^{3}

Minimum (- 3, - 106), Maximum (3, 110)

Solution steps

f^{'} (x) = - 6 x^{2} + 54

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

2 + 54 x - 2 x^{3} : - 106

Minimum (- 3, - 106)

Plug

x = 3

into

2 + 54 x - 2 x^{3} : 110

Maximum (3, 110)

Minimum (- 3, - 106), Maximum (3, 110)

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

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

f (x) = 2 x^{3} - 9 x^{2} - 12 x - 1

f (x) = x^{3} (x + 4)

f (x, z) = x^{3} + z^{3} - 3 x - 3 z

What is the extreme f(x)=2+54x-2x^3 ?
The extreme f(x)=2+54x-2x^3 is Minimum(-3,-106),Maximum(3,110)