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Popular Functions >

extreme x^{2/3}(x-5)

Solution

extreme

Solution

Maximum (0, 0), Minimum (2, - 3 \cdot 2^{\frac{2}{3}})

Solution steps

f^{'} (x) = \frac{5 ( x - 2 )}{3 x ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

x^{\frac{2}{3}} (x - 5) : 0

Maximum (0, 0)

Plug

x = 2

into

x^{\frac{2}{3}} (x - 5) : - 3 \cdot 2^{\frac{2}{3}}

Minimum (2, - 3 \cdot 2^{\frac{2}{3}})

Maximum (0, 0), Minimum (2, - 3 \cdot 2^{\frac{2}{3}})

Graph

Popular Examples

extreme f(x)=100x(2x+3)(x-5)

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

extreme f(x)=x^3+12x

extreme f(x)=2x^3-6x,0<= x<= 3

extreme (x^4)/(x^2-1)

Frequently Asked Questions (FAQ)

What is the extreme x^{2/3}(x-5) ?
The extreme x^{2/3}(x-5) is Maximum(0,0),Minimum(2,-3*2^{2/3})