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

The extreme f(x)=3+81x-3x^3 is Minimum(-3,-159),Maximum(3,165)

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

extreme points

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

Minimum (- 3, - 159), Maximum (3, 165)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

3 + 81 x - 3 x^{3} : - 159

Minimum (- 3, - 159)

Plug

x = 3

into

3 + 81 x - 3 x^{3} : 165

Maximum (3, 165)

Minimum (- 3, - 159), Maximum (3, 165)

f (x, y) = 20 x y - x^{3} - 10 y^{2}

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

f (x) = x^{2} - 5

f (x, y) = x^{2} + x y + y^{2} - 25 y + 208

f (x) = x^{\frac{2}{3}}, - 1 \leq x \leq 2

What is the extreme f(x)=3+81x-3x^3 ?
The extreme f(x)=3+81x-3x^3 is Minimum(-3,-159),Maximum(3,165)