What is the extreme 3x^2-6x-9,0<= x<= 4 ?

The extreme 3x^2-6x-9,0<= x<= 4 is Maximum(0,-9),Minimum(1,-12),Maximum(4,15)

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extreme 3x^2-6x-9,0<= x<= 4

extreme points

3 x^{2} - 6 x - 9, 0 \leq x \leq 4

Maximum (0, - 9), Minimum (1, - 12), Maximum (4, 15)

Solution steps

Find the critical points:

x = 0, x = 1, x = 4

Domain of

3 x^{2} - 6 x - 9, 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

3 x^{2} - 6 x - 9 \Rightarrow y = - 9

Maximum (0, - 9)

Plug the extreme point

x = 1

into

3 x^{2} - 6 x - 9 \Rightarrow y = - 12

Minimum (1, - 12)

Plug the extreme point

x = 4

into

3 x^{2} - 6 x - 9 \Rightarrow y = 15

Maximum (4, 15)

Maximum (0, - 9), Minimum (1, - 12), Maximum (4, 15)

\frac{( 1 - x ^{2} ) ^{3}}{x ^{3}}

121000 x - \frac{1000}{28} x^{2}

f (x) = - \frac{8}{3} x^{3} + 4 x^{2} + 48 x + 9

f (x) = 1400 x - 2 x^{2}

100 x + y

What is the extreme 3x^2-6x-9,0<= x<= 4 ?
The extreme 3x^2-6x-9,0<= x<= 4 is Maximum(0,-9),Minimum(1,-12),Maximum(4,15)