What is the extreme f(x)=x^{4/5}(x+1) ?

The extreme f(x)=x^{4/5}(x+1) is Maximum(-4/9 ,(5(-4/9)^{4/5})/9),Minimum(0,0)

Popular >

extreme f(x)=x^{4/5}(x+1)

extreme points

f (x) = x^{\frac{4}{5}} (x + 1)

Maximum - \frac{4}{9}, \frac{5 ( - \frac{4}{9} ) ^{\frac{4}{5}}}{9}, Minimum (0, 0)

Solution steps

f^{'} (x) = \frac{9 x + 4}{5 x ^{\frac{1}{5}}}

Find intervals:

Increasing

: - \infty < x < - \frac{4}{9},

Decreasing

: - \frac{4}{9} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{4}{9}

into

x^{\frac{4}{5}} (x + 1) : \frac{5 ( - \frac{4}{9} ) ^{\frac{4}{5}}}{9}

Maximum - \frac{4}{9}, \frac{5 ( - \frac{4}{9} ) ^{\frac{4}{5}}}{9}

Plug

x = 0

into

x^{\frac{4}{5}} (x + 1) : 0

Minimum (0, 0)

Maximum - \frac{4}{9}, \frac{5 ( - \frac{4}{9} ) ^{\frac{4}{5}}}{9}, Minimum (0, 0)

f (x) = x^{3} - 3 x, - 2 \leq x \leq 2

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

f (x, y) = 13 x e^{y}

y = - x^{2} + 4

y = \frac{x ^{4} + 1}{x ^{2}}

What is the extreme f(x)=x^{4/5}(x+1) ?
The extreme f(x)=x^{4/5}(x+1) is Maximum(-4/9 ,(5(-4/9)^{4/5})/9),Minimum(0,0)