What is the extreme f(x)=x^2-10x-1,2<= x<= 6 ?

The extreme f(x)=x^2-10x-1,2<= x<= 6 is Maximum(2,-17),Minimum(5,-26),Maximum(6,-25)

extreme f(x)=x^2-10x-1,2<= x<= 6

extreme points

f (x) = x^{2} - 10 x - 1, 2 \leq x \leq 6

Maximum (2, - 17), Minimum (5, - 26), Maximum (6, - 25)

Solution steps

Find the critical points:

x = 2, x = 5, x = 6

Domain of

x^{2} - 10 x - 1, 2 \leq x \leq 6 : 2 \leq x \leq 6

Find intervals:

Decreasing

: 2 < x < 5,

Increasing

: 5 < x < 6

Plug the extreme point

x = 2

into

x^{2} - 10 x - 1 \Rightarrow y = - 17

Maximum (2, - 17)

Plug the extreme point

x = 5

into

x^{2} - 10 x - 1 \Rightarrow y = - 26

Minimum (5, - 26)

Plug the extreme point

x = 6

into

x^{2} - 10 x - 1 \Rightarrow y = - 25

Maximum (6, - 25)

Maximum (2, - 17), Minimum (5, - 26), Maximum (6, - 25)

f (x) = 3 3 x^{3} + 24

3 x (28 - x)

f (x) = x^{3} + 15 x - 9

f (x) = x^{3} - 2 x^{2} - 15 x + 52.2

f (x) = 3 x^{2} - 5 y^{2} - 255 x + 70 y + 23

What is the extreme f(x)=x^2-10x-1,2<= x<= 6 ?
The extreme f(x)=x^2-10x-1,2<= x<= 6 is Maximum(2,-17),Minimum(5,-26),Maximum(6,-25)