What is the extreme f(x)=81x-3x^3 ?

The extreme f(x)=81x-3x^3 is Minimum(-3,-162),Maximum(3,162)

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extreme f(x)=81x-3x^3

extreme points

f (x) = 81 x - 3 x^{3}

Minimum (- 3, - 162), Maximum (3, 162)

Solution steps

f^{'} (x) = 81 - 9 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

81 x - 3 x^{3} : - 162

Minimum (- 3, - 162)

Plug

x = 3

into

81 x - 3 x^{3} : 162

Maximum (3, 162)

Minimum (- 3, - 162), Maximum (3, 162)

F (x, y) = y^{2} - x^{2}

f (x, y) = - 6 x^{2} - 3 x y - 3 y^{2} - 69 x - 9 y + 7

x^{3} - 3 x - 2

x^{3} - 3 x - 3

f (x) = 4 sin (∣ x ∣), - 2 π \leq x \leq 2 π

What is the extreme f(x)=81x-3x^3 ?
The extreme f(x)=81x-3x^3 is Minimum(-3,-162),Maximum(3,162)