What is the extreme f(x)=6x-0.2x^2,0<= x<= 30 ?

The extreme f(x)=6x-0.2x^2,0<= x<= 30 is Minimum(0,0),Maximum(15,45),Minimum(30,0)

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extreme f(x)=6x-0.2x^2,0<= x<= 30

extreme points

f (x) = 6 x - 0.2 x^{2}, 0 \leq x \leq 30

Minimum (0, 0), Maximum (15, 45), Minimum (30, 0)

Solution steps

Find the critical points:

x = 0, x = 15, x = 30

Domain of

6 x - 0.2 x^{2}, 0 \leq x \leq 30 : 0 \leq x \leq 30

Find intervals:

Increasing

: 0 < x < 15,

Decreasing

: 15 < x < 30

Plug the extreme point

x = 0

into

6 x - 0.2 x^{2} \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = 15

into

6 x - 0.2 x^{2} \Rightarrow y = 45

Maximum (15, 45)

Plug the extreme point

x = 30

into

6 x - 0.2 x^{2} \Rightarrow y = 0

Minimum (30, 0)

Minimum (0, 0), Maximum (15, 45), Minimum (30, 0)

5 x^{5} - 3 x^{4} + 2

f (x) = 4 - x, - 3 \leq x \leq 3

f (x, y) = (x^{2} - 9)^{2} + (y^{2} - 36)^{2}

f (x) = - 3 x^{2} - 12 x + 24 y^{2} + 12 y = 0

f (x) = 7 x - 5

What is the extreme f(x)=6x-0.2x^2,0<= x<= 30 ?
The extreme f(x)=6x-0.2x^2,0<= x<= 30 is Minimum(0,0),Maximum(15,45),Minimum(30,0)