What is the extreme f(x)=x^7(x+5)^8,-10<= x<= 10 ?

The extreme f(x)=x^7(x+5)^8,-10<= x<= 10 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x^7(x+5)^8,-10<= x<= 10

extreme points

f (x) = x^{7} (x + 5)^{8}, - 10 \leq x \leq 10

Minimum (- 10, - 5^{15} \cdot 128), Maximum (- 5, 0), Minimum (- \frac{7}{3}, - \frac{1.38168 E 13}{14348907}), Saddle (0, 0), Maximum (10, 5^{15} \cdot 839808)

Solution steps

Find the critical points:

x = - 10, x = - 5, x = - \frac{7}{3}, x = 0, x = 10

Domain of

x^{7} (x + 5)^{8}, - 10 \leq x \leq 10 : - 10 \leq x \leq 10

Find intervals:

Increasing

: - 10 < x < - 5,

Decreasing

: - 5 < x < - \frac{7}{3},

Increasing

: - \frac{7}{3} < x < 0,

Increasing

: 0 < x < 10

Plug the extreme point

x = - 10

into

x^{7} (x + 5)^{8} \Rightarrow y = - 5^{15} 128

Minimum (- 10, - 5^{15} \cdot 128)

Plug the extreme point

x = - 5

into

x^{7} (x + 5)^{8} \Rightarrow y = 0

Maximum (- 5, 0)

Plug the extreme point

x = - \frac{7}{3}

into

x^{7} (x + 5)^{8} \Rightarrow y = - \frac{1.38168 E 13}{14348907}

Minimum (- \frac{7}{3}, - \frac{1.38168 E 13}{14348907})

Plug the extreme point

x = 0

into

x^{7} (x + 5)^{8} \Rightarrow y = 0

Saddle (0, 0)

Plug the extreme point

x = 10

into

x^{7} (x + 5)^{8} \Rightarrow y = 5^{15} 839808

Maximum (10, 5^{15} \cdot 839808)

Minimum (- 10, - 5^{15} \cdot 128), Maximum (- 5, 0), Minimum (- \frac{7}{3}, - \frac{1.38168 E 13}{14348907}), Saddle (0, 0), Maximum (10, 5^{15} \cdot 839808)

g (x) = x^{3} - 9 x

(x^{2} - 1)^{3}, - 1 \leq x \leq 6

x \cdot e^{- 2 x^{2}}

f (x) = x^{4} + 4 x^{3} + 10

What is the extreme f(x)=x^7(x+5)^8,-10<= x<= 10 ?
The extreme f(x)=x^7(x+5)^8,-10<= x<= 10 is