What is the extreme f(x)=-x^{2/3}(x-4) ?

The extreme f(x)=-x^{2/3}(x-4) is Minimum(0,0),Maximum(8/5 ,(48)/(5*5^{2/3)})

Popular >

extreme f(x)=-x^{2/3}(x-4)

extreme points

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

Minimum (0, 0), Maximum (\frac{8}{5}, \frac{48}{5 \cdot 5 ^{\frac{2}{3}}})

Solution steps

f^{'} (x) = - \frac{5 x - 8}{3 x ^{\frac{1}{3}}}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{8}{5},

Decreasing

: \frac{8}{5} < x < \infty

Plug

x = 0

into

- x^{\frac{2}{3}} (x - 4) : 0

Minimum (0, 0)

Plug

x = \frac{8}{5}

into

- x^{\frac{2}{3}} (x - 4) : \frac{48}{5 \cdot 5 ^{\frac{2}{3}}}

Maximum (\frac{8}{5}, \frac{48}{5 \cdot 5 ^{\frac{2}{3}}})

Minimum (0, 0), Maximum (\frac{8}{5}, \frac{48}{5 \cdot 5 ^{\frac{2}{3}}})

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

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

f (x) = x^{3} (x - 6)^{4}

f (x) = \frac{2}{3} x^{3} - 2 x^{2} + \frac{44}{3}

f (x) = 2 x^{3} - 24 x^{2} + 72 x + 7

What is the extreme f(x)=-x^{2/3}(x-4) ?
The extreme f(x)=-x^{2/3}(x-4) is Minimum(0,0),Maximum(8/5 ,(48)/(5*5^{2/3)})