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Popular >

extreme x^{1/3}(1-x)

Solution

extreme points

x^{\frac{1}{3}} (1 - x)

Solution

Maximum (\frac{1}{4}, \frac{3}{4 \cdot 4 ^{\frac{1}{3}}})

Solution steps

f^{'} (x) = \frac{- 4 x + 1}{3 x ^{\frac{2}{3}}}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{1}{4},

Decreasing

: \frac{1}{4} < x < \infty

Plug

x = \frac{1}{4}

into

x^{\frac{1}{3}} (1 - x) : \frac{3}{4 \cdot 4 ^{\frac{1}{3}}}

Maximum (\frac{1}{4}, \frac{3}{4 \cdot 4 ^{\frac{1}{3}}})

Popular Examples

extreme x^2-2xy+3y^2-12y extreme points

x^{2} - 2 x y + 3 y^{2} - 12 y

extreme f(x)=2x^3+4x^2+2/1 x extreme points

f (x) = 2 x^{3} + 4 x^{2} + \frac{2}{1} x

extreme f(x)=2x+(32)/x ,x\ne 0 extreme points

f (x) = 2 x + \frac{32}{x}, x \neq = 0

extreme f(24/13 , 88/39)=3xy-4x^2-3y^2+8x+8y-4 extreme points

f (\frac{24}{13}, \frac{88}{39}) = 3 x y - 4 x^{2} - 3 y^{2} + 8 x + 8 y - 4

extreme-x^3+75x+80 extreme points

- x^{3} + 75 x + 80

Frequently Asked Questions (FAQ)

What is the extreme x^{1/3}(1-x) ?
The extreme x^{1/3}(1-x) is Maximum(1/4 , 3/(4*4^{1/3)})