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Popular >

extreme 6x^4+32x^3

Solution

extreme points

6 x^{4} + 32 x^{3}

Solution

Minimum (- 4, - 512), Saddle (0, 0)

Solution steps

f^{'} (x) = 24 x^{3} + 96 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 4

into

6 x^{4} + 32 x^{3} : - 512

Minimum (- 4, - 512)

Plug

x = 0

into

6 x^{4} + 32 x^{3} : 0

Saddle (0, 0)

Minimum (- 4, - 512), Saddle (0, 0)

Popular Examples

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f (x) = x (20 - 43 + 2 x) (\frac{43}{2} - x)

extreme x^4-2x^2-2 extreme points

x^{4} - 2 x^{2} - 2

extreme x^4-2x^2+1 extreme points

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extreme y=6sqrt(3)x+12cos(x)extreme points

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extreme f(x,y)=x^2+7y^2+x-6y+4 extreme points

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Frequently Asked Questions (FAQ)

What is the extreme 6x^4+32x^3 ?
The extreme 6x^4+32x^3 is Minimum(-4,-512),Saddle(0,0)