What is the extreme 9x^3-54x^2+81x+13,-6<= x<= 2 ?

The extreme 9x^3-54x^2+81x+13,-6<= x<= 2 is Minimum(-6,-4361),Maximum(1,49),Minimum(2,31)

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extreme 9x^3-54x^2+81x+13,-6<= x<= 2

extreme points

9 x^{3} - 54 x^{2} + 81 x + 13, - 6 \leq x \leq 2

Minimum (- 6, - 4361), Maximum (1, 49), Minimum (2, 31)

Solution steps

Find the critical points:

x = - 6, x = 1, x = 2

Domain of

9 x^{3} - 54 x^{2} + 81 x + 13, - 6 \leq x \leq 2 : - 6 \leq x \leq 2

Find intervals:

Increasing

: - 6 < x < 1,

Decreasing

: 1 < x < 2

Plug the extreme point

x = - 6

into

9 x^{3} - 54 x^{2} + 81 x + 13 \Rightarrow y = - 4361

Minimum (- 6, - 4361)

Plug the extreme point

x = 1

into

9 x^{3} - 54 x^{2} + 81 x + 13 \Rightarrow y = 49

Maximum (1, 49)

Plug the extreme point

x = 2

into

9 x^{3} - 54 x^{2} + 81 x + 13 \Rightarrow y = 31

Minimum (2, 31)

Minimum (- 6, - 4361), Maximum (1, 49), Minimum (2, 31)

f (x) = \frac{( x ^{2} - 121 )}{2 x ^{2}}

\frac{( x ^{2} + 16 )}{( x - 3 )}

540 x - 5 x^{3}

f (x) = 232 x - 5000 - x^{2}

What is the extreme 9x^3-54x^2+81x+13,-6<= x<= 2 ?
The extreme 9x^3-54x^2+81x+13,-6<= x<= 2 is Minimum(-6,-4361),Maximum(1,49),Minimum(2,31)