What is the extreme f(x)=3+3x-3x^2,0<= x<= 3 ?

The extreme f(x)=3+3x-3x^2,0<= x<= 3 is Minimum(0,3),Maximum(1/2 , 15/4),Minimum(3,-15)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=3+3x-3x^2,0<= x<= 3

extreme points

f (x) = 3 + 3 x - 3 x^{2}, 0 \leq x \leq 3

Minimum (0, 3), Maximum (\frac{1}{2}, \frac{15}{4}), Minimum (3, - 15)

Solution steps

Find the critical points:

x = 0, x = \frac{1}{2}, x = 3

Domain of

3 + 3 x - 3 x^{2}, 0 \leq x \leq 3 : 0 \leq x \leq 3

Find intervals:

Increasing

: 0 < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < 3

Plug the extreme point

x = 0

into

3 + 3 x - 3 x^{2} \Rightarrow y = 3

Minimum (0, 3)

Plug the extreme point

x = \frac{1}{2}

into

3 + 3 x - 3 x^{2} \Rightarrow y = \frac{15}{4}

Maximum (\frac{1}{2}, \frac{15}{4})

Plug the extreme point

x = 3

into

3 + 3 x - 3 x^{2} \Rightarrow y = - 15

Minimum (3, - 15)

Minimum (0, 3), Maximum (\frac{1}{2}, \frac{15}{4}), Minimum (3, - 15)

100

f (x) = \frac{1}{x ^{2} + 1}

x^{2} + \frac{405000}{x}

\frac{2 x ^{2} - 14 x + 24}{x ^{2} + 6 x + 40}

f (x) = x (5 - x) (8 - x), 0 < x < 5

What is the extreme f(x)=3+3x-3x^2,0<= x<= 3 ?
The extreme f(x)=3+3x-3x^2,0<= x<= 3 is Minimum(0,3),Maximum(1/2 , 15/4),Minimum(3,-15)