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Popular >

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

Solution

extreme points

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

Solution

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)

Popular Examples

intercepts of (x^2-2x+4)/(x-2)intercepts

\frac{x ^{2} - 2 x + 4}{x - 2}

asymptotes of f(x)=x+1/x asymptotes

f (x) = x + \frac{1}{x}

domain of f(x)= 3/(x-8)domain

f (x) = \frac{3}{x - 8}

intercepts of 2x^2-4x-1 intercepts

2 x^{2} - 4 x - 1

asymptotes of e^{x-2}asymptotes

e^{x - 2}

Frequently Asked Questions (FAQ)

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