What is the extreme f(x)=x^7(x+4)^4,-10<= x<= 13 ?

The extreme f(x)=x^7(x+4)^4,-10<= x<= 13 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+4)^4,-10<= x<= 13

extreme points

f (x) = x^{7} (x + 4)^{4}, - 10 \leq x \leq 13

Minimum (- 10, - 12960000000), Maximum (- 4, 0), Minimum (- \frac{28}{11}, - \frac{2 ^{30} \cdot 823543}{1 1 ^{11}}), Saddle (0, 0), Maximum (13, 5240818888357)

Solution steps

Find the critical points:

x = - 10, x = - 4, x = - \frac{28}{11}, x = 0, x = 13

Domain of

x^{7} (x + 4)^{4}, - 10 \leq x \leq 13 : - 10 \leq x \leq 13

Find intervals:

Increasing

: - 10 < x < - 4,

Decreasing

: - 4 < x < - \frac{28}{11},

Increasing

: - \frac{28}{11} < x < 0,

Increasing

: 0 < x < 13

Plug the extreme point

x = - 10

into

x^{7} (x + 4)^{4} \Rightarrow y = - 12960000000

Minimum (- 10, - 12960000000)

Plug the extreme point

x = - 4

into

x^{7} (x + 4)^{4} \Rightarrow y = 0

Maximum (- 4, 0)

Plug the extreme point

x = - \frac{28}{11}

into

x^{7} (x + 4)^{4} \Rightarrow y = - \frac{2 ^{30} 823543}{1 1 ^{11}}

Minimum (- \frac{28}{11}, - \frac{2 ^{30} \cdot 823543}{1 1 ^{11}})

Plug the extreme point

x = 0

into

x^{7} (x + 4)^{4} \Rightarrow y = 0

Saddle (0, 0)

Plug the extreme point

x = 13

into

x^{7} (x + 4)^{4} \Rightarrow y = 5240818888357

Maximum (13, 5240818888357)

Minimum (- 10, - 12960000000), Maximum (- 4, 0), Minimum (- \frac{28}{11}, - \frac{2 ^{30} \cdot 823543}{1 1 ^{11}}), Saddle (0, 0), Maximum (13, 5240818888357)

y = x^{4} - 8 x^{2} + 5

f (x) = (x - 7) e^{x}

y (x, t) = 3 x + 2 a t (3.4)

f (x) = - 3 (x + 2) e^{4 x}

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

What is the extreme f(x)=x^7(x+4)^4,-10<= x<= 13 ?
The extreme f(x)=x^7(x+4)^4,-10<= x<= 13 is