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Popular >

extreme x^4-12x^3

Solution

extreme points

x^{4} - 12 x^{3}

Solution

Saddle (0, 0), Minimum (9, - 2187)

Solution steps

f^{'} (x) = 4 x^{3} - 36 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = 0

into

x^{4} - 12 x^{3} : 0

Saddle (0, 0)

Plug

x = 9

into

x^{4} - 12 x^{3} : - 2187

Minimum (9, - 2187)

Saddle (0, 0), Minimum (9, - 2187)

Popular Examples

domain of (6x)/(x-5)domain

\frac{6 x}{x - 5}

line (-4,6),(6,4)line

(- 4, 6), (6, 4)

asymptotes of 2/(x-1)+1 asymptotes

\frac{2}{x - 1} + 1

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

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

critical (x-8)/(x+6)critical points

\frac{x - 8}{x + 6}

Frequently Asked Questions (FAQ)

What is the extreme x^4-12x^3 ?
The extreme x^4-12x^3 is Saddle(0,0),Minimum(9,-2187)