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Popular >

extreme x^3-16x^2+12x-4

Solution

extreme points

x^{3} - 16 x^{2} + 12 x - 4

Solution

Maximum (\frac{2 ( 8 - 55 )}{3}, \frac{1096 55 - 8192}{27} + 60 - 855), Minimum (\frac{2 ( 8 + 55 )}{3}, \frac{- 8192 - 1096 55}{27} + 60 + 855)

Solution steps

f^{'} (x) = 3 x^{2} - 32 x + 12

Find intervals:

Increasing

: - \infty < x < \frac{- 2 55 + 16}{3},

Decreasing

: \frac{- 2 55 + 16}{3} < x < \frac{2 55 + 16}{3},

Increasing

: \frac{2 55 + 16}{3} < x < \infty

Plug

x = \frac{2 ( 8 - 55 )}{3}

into

x^{3} - 16 x^{2} + 12 x - 4 : \frac{1096 55 - 8192}{27} + 60 - 855

Maximum (\frac{2 ( 8 - 55 )}{3}, \frac{1096 55 - 8192}{27} + 60 - 855)

Plug

x = \frac{2 ( 8 + 55 )}{3}

into

x^{3} - 16 x^{2} + 12 x - 4 : \frac{- 8192 - 1096 55}{27} + 60 + 855

Minimum (\frac{2 ( 8 + 55 )}{3}, \frac{- 8192 - 1096 55}{27} + 60 + 855)

Maximum (\frac{2 ( 8 - 55 )}{3}, \frac{1096 55 - 8192}{27} + 60 - 855), Minimum (\frac{2 ( 8 + 55 )}{3}, \frac{- 8192 - 1096 55}{27} + 60 + 855)

Popular Examples

domain of f(x)=-9 domain

f (x) = - 9

extreme f(x)=-2/(x^2-16)extreme points

f (x) = - \frac{2}{x ^{2} - 16}

inverse of f(x)=2x^3+5 inverse

f (x) = 2 x^{3} + 5

inverse of f(x)=(5x+9)/(x+5)inverse

f (x) = \frac{5 x + 9}{x + 5}

extreme f(x)=3x^4+8x^3 extreme points

f (x) = 3 x^{4} + 8 x^{3}

Frequently Asked Questions (FAQ)

What is the extreme x^3-16x^2+12x-4 ?
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