en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=3x^3+92x^2-54x+1

Solution

extreme points

f (x) = 3 x^{3} + 92 x^{2} - 54 x + 1

Solution

Maximum (- \frac{92 + 5 358}{9}, \frac{1557376 + 82210 358}{243} + 553 + 30358), Minimum (\frac{- 92 + 5 358}{9}, \frac{1557376 - 82210 358}{243} + 553 - 30358)

Solution steps

f^{'} (x) = 9 x^{2} + 184 x - 54

Find intervals:

Increasing

: - \infty < x < \frac{- 5 358 - 92}{9},

Decreasing

: \frac{- 5 358 - 92}{9} < x < \frac{5 358 - 92}{9},

Increasing

: \frac{5 358 - 92}{9} < x < \infty

Plug

x = - \frac{92 + 5 358}{9}

into

3 x^{3} + 92 x^{2} - 54 x + 1 : \frac{1557376 + 82210 358}{243} + 553 + 30358

Maximum (- \frac{92 + 5 358}{9}, \frac{1557376 + 82210 358}{243} + 553 + 30358)

Plug

x = \frac{- 92 + 5 358}{9}

into

3 x^{3} + 92 x^{2} - 54 x + 1 : \frac{1557376 - 82210 358}{243} + 553 - 30358

Minimum (\frac{- 92 + 5 358}{9}, \frac{1557376 - 82210 358}{243} + 553 - 30358)

Maximum (- \frac{92 + 5 358}{9}, \frac{1557376 + 82210 358}{243} + 553 + 30358), Minimum (\frac{- 92 + 5 358}{9}, \frac{1557376 - 82210 358}{243} + 553 - 30358)

Popular Examples

extreme y=-1/3 e^{-3x}x-10/9 e^{-3x}extreme points

y = - \frac{1}{3} e^{- 3 x} x - \frac{10}{9} e^{- 3 x}

extreme f(y)=6xy-6y extreme points

f (y) = 6 x y - 6 y

extreme f(x)=0.1x^2=1.2x+98.5 extreme points

f (x) = 0.1 x^{2} = 1.2 x + 98.5

extreme f(x)=x(7-x)(30-2x)extreme points

f (x) = x (7 - x) (30 - 2 x)

extreme S(a,b)=2pi(a+b)extreme points

S (a, b) = 2 π (a + b)

Frequently Asked Questions (FAQ)

What is the extreme f(x)=3x^3+92x^2-54x+1 ?
The extreme f(x)=3x^3+92x^2-54x+1 is