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Popular >

extreme y=x^3-4x^2

Solution

extreme points

y = x^{3} - 4 x^{2}

Solution

Maximum (0, 0), Minimum (\frac{8}{3}, - \frac{256}{27})

Solution steps

f^{'} (x) = 3 x^{2} - 8 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{8}{3},

Increasing

: \frac{8}{3} < x < \infty

Plug

x = 0

into

x^{3} - 4 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{8}{3}

into

x^{3} - 4 x^{2} : - \frac{256}{27}

Minimum (\frac{8}{3}, - \frac{256}{27})

Maximum (0, 0), Minimum (\frac{8}{3}, - \frac{256}{27})

Popular Examples

extreme f(x,y)=3x^3+y^2-9x+4y extreme points

f (x, y) = 3 x^{3} + y^{2} - 9 x + 4 y

extreme f(x)=(-2x^2+14x-24)/(x^2+2x)extreme points

f (x) = \frac{- 2 x ^{2} + 14 x - 24}{x ^{2} + 2 x}

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

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

extreme f(x)=1-x-x^2 extreme points

f (x) = 1 - x - x^{2}

extreme f(x)=32y^2+x^2-x^2y extreme points

f (x) = 32 y^{2} + x^{2} - x^{2} y

Frequently Asked Questions (FAQ)

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