What is the extreme f(x)=7(x^2+1)^2(x-5)^3 ?

The extreme f(x)=7(x^2+1)^2(x-5)^3 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=7(x^2+1)^2(x-5)^3

extreme points

f (x) = 7 (x^{2} + 1)^{2} (x - 5)^{3}

Maximum (\frac{10 - 79}{7}, \frac{33212864 79 - 290474405}{117649} - 875), Minimum (\frac{10 + 79}{7}, \frac{- 33212864 79 - 290474405}{117649} - 875), Saddle (5, 0)

Solution steps

Find the critical points:

x = \frac{10 - 79}{7}, x = \frac{10 + 79}{7}, x = 5

Domain of

7 (x^{2} + 1)^{2} (x - 5)^{3} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < \frac{10 - 79}{7},

Decreasing

: \frac{10 - 79}{7} < x < \frac{10 + 79}{7},

Increasing

: \frac{10 + 79}{7} < x < 5,

Increasing

: 5 < x < \infty

Plug the extreme point

x = \frac{10 - 79}{7}

into

7 (x^{2} + 1)^{2} (x - 5)^{3} \Rightarrow y = \frac{33212864 79 - 290474405}{117649} - 875

Maximum (\frac{10 - 79}{7}, \frac{33212864 79 - 290474405}{117649} - 875)

Plug the extreme point

x = \frac{10 + 79}{7}

into

7 (x^{2} + 1)^{2} (x - 5)^{3} \Rightarrow y = \frac{- 33212864 79 - 290474405}{117649} - 875

Minimum (\frac{10 + 79}{7}, \frac{- 33212864 79 - 290474405}{117649} - 875)

Plug the extreme point

x = 5

into

7 (x^{2} + 1)^{2} (x - 5)^{3} \Rightarrow y = 0

Saddle (5, 0)

Maximum (\frac{10 - 79}{7}, \frac{33212864 79 - 290474405}{117649} - 875), Minimum (\frac{10 + 79}{7}, \frac{- 33212864 79 - 290474405}{117649} - 875), Saddle (5, 0)

f (x) = 9 x^{4} - 4 x^{3}, - 3 \leq x \leq 3

f (x) = (x^{2} - 5 x + 4) (x)

f (x) = 2600 + 2 x + 0.001 x^{2}

f (x) = x^{3} - 12 x^{2} - 27 x + 9 (- 2)

f (x) = 13 + 7 x + x^{2}

What is the extreme f(x)=7(x^2+1)^2(x-5)^3 ?
The extreme f(x)=7(x^2+1)^2(x-5)^3 is