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Popular >

extreme x^4-4x^3+14

Solution

extreme points

x^{4} - 4 x^{3} + 14

Solution

Saddle (0, 14), Minimum (3, - 13)

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} + 14 : 14

Saddle (0, 14)

Plug

x = 3

into

x^{4} - 4 x^{3} + 14 : - 13

Minimum (3, - 13)

Saddle (0, 14), Minimum (3, - 13)

Popular Examples

extreme f(x)=(2x^2+18)/x extreme points

f (x) = \frac{2 x ^{2} + 18}{x}

extreme f(x)=-x^2-15.9x-57 extreme points

f (x) = - x^{2} - 15.9 x - 57

extreme f(x,y)=x^2+y^2-4x+2y extreme points

f (x, y) = x^{2} + y^{2} - 4 x + 2 y

extreme f(x)=(-x^2-10x-13)/(x+9)extreme points

f (x) = \frac{- x ^{2} - 10 x - 13}{x + 9}

extreme x^3-9x^2+1 extreme points

x^{3} - 9 x^{2} + 1

Frequently Asked Questions (FAQ)

What is the extreme x^4-4x^3+14 ?
The extreme x^4-4x^3+14 is Saddle(0,14),Minimum(3,-13)