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

The extreme f(x)=f(x)=3x-x^3 is Minimum(-1,-2),Maximum(1,2)

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

extreme points

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

Minimum (- 1, - 2), Maximum (1, 2)

Solution steps

f^{'} (x) = 3 - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

3 x - x^{3} : - 2

Minimum (- 1, - 2)

Plug

x = 1

into

3 x - x^{3} : 2

Maximum (1, 2)

Minimum (- 1, - 2), Maximum (1, 2)

f (x) = \frac{1}{x ^{2} + 4}

y = - x^{2} + 25

f (x) = 3 + 7 x + 175 x^{- 1}

\frac{1}{x ^{2} - x - 6}

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

What is the extreme f(x)=f(x)=3x-x^3 ?
The extreme f(x)=f(x)=3x-x^3 is Minimum(-1,-2),Maximum(1,2)