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Popular >

extreme x^3-8x^2+16x

Solution

extreme points

x^{3} - 8 x^{2} + 16 x

Solution

Maximum (\frac{4}{3}, \frac{256}{27}), Minimum (4, 0)

Solution steps

f^{'} (x) = 3 x^{2} - 16 x + 16

Find intervals:

Increasing

: - \infty < x < \frac{4}{3},

Decreasing

: \frac{4}{3} < x < 4,

Increasing

: 4 < x < \infty

Plug

x = \frac{4}{3}

into

x^{3} - 8 x^{2} + 16 x : \frac{256}{27}

Maximum (\frac{4}{3}, \frac{256}{27})

Plug

x = 4

into

x^{3} - 8 x^{2} + 16 x : 0

Minimum (4, 0)

Maximum (\frac{4}{3}, \frac{256}{27}), Minimum (4, 0)

Popular Examples

extreme f(x,y)=15x^2-2x^3+3y^2+6xy extreme points

f (x, y) = 15 x^{2} - 2 x^{3} + 3 y^{2} + 6 x y

extreme 4x^{3/4}-x,0<= x<= 256 extreme points

4 x^{\frac{3}{4}} - x, 0 \leq x \leq 256

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\frac{2 x + 1}{x ^{2} + 12 x + 48}

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extreme 2cos(x)-2 extreme points

2 cos (x) - 2

Frequently Asked Questions (FAQ)

What is the extreme x^3-8x^2+16x ?
The extreme x^3-8x^2+16x is Maximum(4/3 , 256/27),Minimum(4,0)