What is the extreme f(x)=5+54x-2x^3 ?

The extreme f(x)=5+54x-2x^3 is Minimum(-3,-103),Maximum(3,113)

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extreme f(x)=5+54x-2x^3

extreme points

f (x) = 5 + 54 x - 2 x^{3}

Minimum (- 3, - 103), Maximum (3, 113)

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

5 + 54 x - 2 x^{3} : - 103

Minimum (- 3, - 103)

Plug

x = 3

into

5 + 54 x - 2 x^{3} : 113

Maximum (3, 113)

Minimum (- 3, - 103), Maximum (3, 113)

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

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

K (y, z) = 32 yz

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

f (x) = - x^{4} - 8 x^{3} - 18 x^{2} + 6

What is the extreme f(x)=5+54x-2x^3 ?
The extreme f(x)=5+54x-2x^3 is Minimum(-3,-103),Maximum(3,113)