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

The extreme f(x)=x^2-x-3,0<= x<= 3 is Maximum(0,-3),Minimum(1/2 ,-13/4),Maximum(3,3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

extreme

Maximum (0, - 3), Minimum (\frac{1}{2}, - \frac{13}{4}), Maximum (3, 3)

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Decreasing

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

Increasing

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

Plug the extreme point

x = 0

into

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

Maximum (0, - 3)

Plug the extreme point

x = \frac{1}{2}

into

x^{2} - x - 3 \Rightarrow y = - \frac{13}{4}

Minimum (\frac{1}{2}, - \frac{13}{4})

Plug the extreme point

x = 3

into

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

Maximum (3, 3)

Maximum (0, - 3), Minimum (\frac{1}{2}, - \frac{13}{4}), Maximum (3, 3)

What is the extreme f(x)=x^2-x-3,0<= x<= 3 ?
The extreme f(x)=x^2-x-3,0<= x<= 3 is Maximum(0,-3),Minimum(1/2 ,-13/4),Maximum(3,3)