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Popular >

extreme f(x)=3x^2-x^3

Solution

extreme points

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

Solution

Minimum (0, 0), Maximum (2, 4)

Solution steps

f^{'} (x) = 6 x - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

3 x^{2} - x^{3} : 0

Minimum (0, 0)

Plug

x = 2

into

3 x^{2} - x^{3} : 4

Maximum (2, 4)

Minimum (0, 0), Maximum (2, 4)

Popular Examples

asymptotes of f(x)=(x-6)/(x+6)asymptotes

f (x) = \frac{x - 6}{x + 6}

simplify (4.3)(1.2)simplify

(4.3) (1.2)

intercepts of f(x)=2x-3y=6 intercepts

f (x) = 2 x - 3 y = 6

asymptotes of (x^4)/((1+x)^3)asymptotes

\frac{x ^{4}}{( 1 + x ) ^{3}}

intercepts of f(x)=2x-4y=12 intercepts

f (x) = 2 x - 4 y = 12

Frequently Asked Questions (FAQ)

What is the extreme f(x)=3x^2-x^3 ?
The extreme f(x)=3x^2-x^3 is Minimum(0,0),Maximum(2,4)