en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme y=x^{2/7}(x^2-5)

Solution

extreme

Solution

Minimum - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}, - \frac{35 ( - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{8}, Maximum (0, 0), Minimum (\frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}, - \frac{35 \cdot 5 ^{\frac{1}{7}}}{8 \cdot 2 ^{\frac{3}{7}}})

Solution steps

f^{'} (x) = \frac{2 ( 2 ^{1 + \frac{1}{2}} x + 5 ^{\frac{1}{2}} ) ( 2 ^{1 + \frac{1}{2}} x - 5 ^{\frac{1}{2}} )}{7 x ^{\frac{5}{7}}}

Find intervals:

Decreasing

: - \infty < x < - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}},

Increasing

: - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} < x < 0,

Decreasing

: 0 < x < \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}},

Increasing

: \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} < x < \infty

Plug

x = - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}

into

x^{\frac{2}{7}} (x^{2} - 5) : - \frac{35 ( - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{8}

Minimum - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}, - \frac{35 ( - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{8}

Plug

x = 0

into

x^{\frac{2}{7}} (x^{2} - 5) : 0

Maximum (0, 0)

Plug

x = \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}

into

x^{\frac{2}{7}} (x^{2} - 5) : - \frac{35 \cdot 5 ^{\frac{1}{7}}}{8 \cdot 2 ^{\frac{3}{7}}}

Minimum (\frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}, - \frac{35 \cdot 5 ^{\frac{1}{7}}}{8 \cdot 2 ^{\frac{3}{7}}})

Minimum - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}, - \frac{35 ( - \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{8}, Maximum (0, 0), Minimum (\frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}, - \frac{35 \cdot 5 ^{\frac{1}{7}}}{8 \cdot 2 ^{\frac{3}{7}}})

Graph

Popular Examples

extreme y=-tu(t-1)+tu(t-2)

extreme f(x)=2x^2+2y^2-8x+16y

extreme f(x)=x^2+y^2-8y+16

extreme x^3(x-1)^2(7x-4)

extreme (x^2+x-2)/(x+3)

Frequently Asked Questions (FAQ)

What is the extreme y=x^{2/7}(x^2-5) ?
The extreme y=x^{2/7}(x^2-5) is