en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme-8x^{5/3}+\sqrt[3]{x}

Solution

extreme points

- 8 x^{\frac{5}{3}} + 3 x

Solution

Minimum (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}), Maximum (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

Solution steps

f^{'} (x) = - \frac{40 x ^{\frac{2}{3}}}{3} + \frac{1}{3 x ^{\frac{2}{3}}}

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{4 0 ^{\frac{3}{4}}},

Increasing

: - \frac{1}{4 0 ^{\frac{3}{4}}} < x < 0,

Increasing

: 0 < x < \frac{1}{4 0 ^{\frac{3}{4}}},

Decreasing

: \frac{1}{4 0 ^{\frac{3}{4}}} < x < \infty

Plug

x = - \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

into

- 8 x^{\frac{5}{3}} + 3 x : - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}

Minimum (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}})

Plug

x = \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

into

- 8 x^{\frac{5}{3}} + 3 x : - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

Maximum (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

Minimum (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}), Maximum (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

Graph

Popular Examples

extreme f(x,y)=2x^3+6xy+3y^2 extreme points

f (x, y) = 2 x^{3} + 6 x y + 3 y^{2}

extreme f(x,y)=16x\sqrt[3]{y}-2x^2-4x-16y+2 extreme points

f (x, y) = 16 x 3 y - 2 x^{2} - 4 x - 16 y + 2

extreme f(x)=cos(5x),-pi/6 <= x<= pi/4 extreme points

f (x) = cos (5 x), - \frac{π}{6} \leq x \leq \frac{π}{4}

extreme f(x)=12x^4-4x^2+6 extreme points

f (x) = 12 x^{4} - 4 x^{2} + 6

extreme f(x)=16sin(2x),-2pi<= x<= 2pi extreme points

f (x) = 16 sin (2 x), - 2 π \leq x \leq 2 π

Frequently Asked Questions (FAQ)

What is the extreme-8x^{5/3}+\sqrt[3]{x} ?
The extreme-8x^{5/3}+\sqrt[3]{x} is