What is the extreme f(x)=x^2-2x,0<= x<= 4 ?

The extreme f(x)=x^2-2x,0<= x<= 4 is Maximum(0,0),Minimum(1,-1),Maximum(4,8)

Popular >

extreme f(x)=x^2-2x,0<= x<= 4

extreme points

f (x) = x^{2} - 2 x, 0 \leq x \leq 4

Maximum (0, 0), Minimum (1, - 1), Maximum (4, 8)

Solution steps

Find the critical points:

x = 0, x = 1, x = 4

Domain of

x^{2} - 2 x, 0 \leq x \leq 4 : 0 \leq x \leq 4

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 4

Plug the extreme point

x = 0

into

x^{2} - 2 x \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 1

into

x^{2} - 2 x \Rightarrow y = - 1

Minimum (1, - 1)

Plug the extreme point

x = 4

into

x^{2} - 2 x \Rightarrow y = 8

Maximum (4, 8)

Maximum (0, 0), Minimum (1, - 1), Maximum (4, 8)

f (x) = x^{3} - x^{2} - 8 x + 8, - 2 \leq x \leq 0

f (x) = \frac{x ^{2} - 11 x + 54}{x - 9}

2 x y

f (x) = \frac{8}{3} x^{3} + 32 x^{2} + 120 x + 9

f (x) = 2 x + ln (x)

What is the extreme f(x)=x^2-2x,0<= x<= 4 ?
The extreme f(x)=x^2-2x,0<= x<= 4 is Maximum(0,0),Minimum(1,-1),Maximum(4,8)