What is the extreme f(x)=4sqrt(x)-x,2<= x<= 8 ?

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

Popular >

extreme f(x)=4sqrt(x)-x,2<= x<= 8

extreme points

f (x) = 4 x - x, 2 \leq x \leq 8

Minimum (2, 42 - 2), Maximum (4, 4), Minimum (8, 82 - 8)

Solution steps

Find the critical points:

x = 2, x = 4, x = 8

Domain of

4 x - x, 2 \leq x \leq 8 : 2 \leq x \leq 8

Find intervals:

Increasing

: 2 < x < 4,

Decreasing

: 4 < x < 8

Plug the extreme point

x = 2

into

4 x - x \Rightarrow y = 42 - 2

Minimum (2, 42 - 2)

Plug the extreme point

x = 4

into

4 x - x \Rightarrow y = 4

Maximum (4, 4)

Plug the extreme point

x = 8

into

4 x - x \Rightarrow y = 82 - 8

Minimum (8, 82 - 8)

Minimum (2, 42 - 2), Maximum (4, 4), Minimum (8, 82 - 8)

f (x) = (x - 9)^{3} (x + 5)^{2}

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

sin (4 x), 0 \leq x \leq \frac{π}{2}

f (x) = \frac{x ^{2} - 4 x + 4}{x - 6}

f (x) = x^{3} - 588 x

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