en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=(8x)^3-(5x)^2-3x

Solution

extreme points

f (x) = (8 x)^{3} - (5 x)^{2} - 3 x

Solution

Maximum (\frac{25 - 5233}{1536}, \frac{5233 5233 - 188425}{3538944}), Minimum (\frac{25 + 5233}{1536}, \frac{- 188425 - 5233 5233}{3538944})

Solution steps

f^{'} (x) = 1536 x^{2} - 50 x - 3

Find intervals:

Increasing

: - \infty < x < \frac{- 5233 + 25}{1536},

Decreasing

: \frac{- 5233 + 25}{1536} < x < \frac{5233 + 25}{1536},

Increasing

: \frac{5233 + 25}{1536} < x < \infty

Plug

x = \frac{25 - 5233}{1536}

into

(8 x)^{3} - (5 x)^{2} - 3 x : \frac{5233 5233 - 188425}{3538944}

Maximum (\frac{25 - 5233}{1536}, \frac{5233 5233 - 188425}{3538944})

Plug

x = \frac{25 + 5233}{1536}

into

(8 x)^{3} - (5 x)^{2} - 3 x : \frac{- 188425 - 5233 5233}{3538944}

Minimum (\frac{25 + 5233}{1536}, \frac{- 188425 - 5233 5233}{3538944})

Maximum (\frac{25 - 5233}{1536}, \frac{5233 5233 - 188425}{3538944}), Minimum (\frac{25 + 5233}{1536}, \frac{- 188425 - 5233 5233}{3538944})

Popular Examples

extreme f(x)=2 extreme points

f (x) = 2

extreme f(x,y)=3x^3+xy^2-2xy+1 extreme points

f (x, y) = 3 x^{3} + x y^{2} - 2 x y + 1

extreme g(x)=x^3-3x^2+3 extreme points

g (x) = x^{3} - 3 x^{2} + 3

extreme f(x,y)=(x^2+y)/(xy-1)extreme points

f (x, y) = \frac{x ^{2} + y}{x y - 1}

extreme f(x,y)=x^2+xy+y^2-3x-6y+1 extreme points

f (x, y) = x^{2} + x y + y^{2} - 3 x - 6 y + 1

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(8x)^3-(5x)^2-3x ?
The extreme f(x)=(8x)^3-(5x)^2-3x is