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

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

Popular >

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

extreme points

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

Maximum (0, 0), Minimum (1, - 2), Maximum (2, 2)

Solution steps

Find the critical points:

x = 0, x = 1, x = 2

Domain of

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

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 2

Plug the extreme point

x = 0

into

x^{3} - 3 x \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 1

into

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

Minimum (1, - 2)

Plug the extreme point

x = 2

into

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

Maximum (2, 2)

Maximum (0, 0), Minimum (1, - 2), Maximum (2, 2)

2 x - x

f (x) = 2 sin (x) - x

f (x) = x^{9} - 3 x^{7} + 2

ln^{2} (x^{2} + x + 1)

f (x) = - x^{3} + 12 x - 11

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