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Popular >

extreme x^4-4x^3+7

Solution

extreme points

x^{4} - 4 x^{3} + 7

Solution

Saddle (0, 7), Minimum (3, - 20)

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} + 7 : 7

Saddle (0, 7)

Plug

x = 3

into

x^{4} - 4 x^{3} + 7 : - 20

Minimum (3, - 20)

Saddle (0, 7), Minimum (3, - 20)

Graph

Popular Examples

extreme x^4-4x^3+4 extreme points

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

extreme f(x)=x^{1/3 (4x^2-14x-224)}extreme points

f (x) = x^{\frac{1}{3} (4 x^{2} - 14 x - 224)}

extreme f(x)=9-x^2-y^2 extreme points

f (x) = 9 - x^{2} - y^{2}

extreme y=3x^2-2x+1 extreme points

y = 3 x^{2} - 2 x + 1

extreme (x^2)/(x^2-25)extreme points

\frac{x ^{2}}{x ^{2} - 25}

Frequently Asked Questions (FAQ)

What is the extreme x^4-4x^3+7 ?
The extreme x^4-4x^3+7 is Saddle(0,7),Minimum(3,-20)