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Popular >

extreme x^4-4x^3+3

Solution

extreme points

x^{4} - 4 x^{3} + 3

Solution

Saddle (0, 3), Minimum (3, - 24)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

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

Saddle (0, 3)

Plug

x = 3

into

x^{4} - 4 x^{3} + 3 : - 24

Minimum (3, - 24)

Saddle (0, 3), Minimum (3, - 24)

Popular Examples

inflection f(x)=-x^3+3x^2-1 inflection points

f (x) = - x^{3} + 3 x^{2} - 1

intercepts of f(x)=-sqrt(x)+3 intercepts

f (x) = - x + 3

periodicity of 4sin(6x-pi)periodicity

4 sin (6 x - π)

domain of f(x)=((x-2)/(x-1))domain

f (x) = (\frac{x - 2}{x - 1})

symmetry 3(x-2)(x+4)symmetry

3 (x - 2) (x + 4)

Frequently Asked Questions (FAQ)

What is the extreme x^4-4x^3+3 ?
The extreme x^4-4x^3+3 is Saddle(0,3),Minimum(3,-24)