en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme f(x)=(x-3)(x+1)(x+5)

Solution

extreme

Solution

Maximum (- \frac{3 + 4}{3}, \frac{128 + 45 3}{3 3} - 15), Minimum (\frac{- 3 + 4 3}{3}, \frac{45 3 - 128}{3 3} - 15)

Solution steps

f^{'} (x) = 3 x^{2} + 6 x - 13

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{3 + 4}{3}

into

(x - 3) (x + 1) (x + 5) : \frac{128 + 45 3}{3 3} - 15

Maximum (- \frac{3 + 4}{3}, \frac{128 + 45 3}{3 3} - 15)

Plug

x = \frac{- 3 + 4 3}{3}

into

(x - 3) (x + 1) (x + 5) : \frac{45 3 - 128}{3 3} - 15

Minimum (\frac{- 3 + 4 3}{3}, \frac{45 3 - 128}{3 3} - 15)

Maximum (- \frac{3 + 4}{3}, \frac{128 + 45 3}{3 3} - 15), Minimum (\frac{- 3 + 4 3}{3}, \frac{45 3 - 128}{3 3} - 15)

Graph

Popular Examples

extreme f(x)=3-x^2

extreme x^2-2x+9

extreme f(x)=x^2log_{7}(x)

extreme U(x,y)=-x^2+8-y^2

extreme f(x)=2x^4+8x^2-8x^3-1

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x-3)(x+1)(x+5) ?
The extreme f(x)=(x-3)(x+1)(x+5) is