What is the extreme f(x)=2x^3+6x^2-144x+2,-6<= x<= 5 ?

The extreme f(x)=2x^3+6x^2-144x+2,-6<= x<= 5 is Maximum(-6,650),Minimum(4,-350),Maximum(5,-318)

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extreme f(x)=2x^3+6x^2-144x+2,-6<= x<= 5

extreme points

f (x) = 2 x^{3} + 6 x^{2} - 144 x + 2, - 6 \leq x \leq 5

Maximum (- 6, 650), Minimum (4, - 350), Maximum (5, - 318)

Solution steps

Find the critical points:

x = - 6, x = 4, x = 5

Domain of

2 x^{3} + 6 x^{2} - 144 x + 2, - 6 \leq x \leq 5 : - 6 \leq x \leq 5

Find intervals:

Decreasing

: - 6 < x < 4,

Increasing

: 4 < x < 5

Plug the extreme point

x = - 6

into

2 x^{3} + 6 x^{2} - 144 x + 2 \Rightarrow y = 650

Maximum (- 6, 650)

Plug the extreme point

x = 4

into

2 x^{3} + 6 x^{2} - 144 x + 2 \Rightarrow y = - 350

Minimum (4, - 350)

Plug the extreme point

x = 5

into

2 x^{3} + 6 x^{2} - 144 x + 2 \Rightarrow y = - 318

Maximum (5, - 318)

Maximum (- 6, 650), Minimum (4, - 350), Maximum (5, - 318)

f (x) = \frac{x ^{3}}{3} + x

f (x) = (9 sin (x) - 9) (2 cos (x) 3)

f (x) = - x^{3} - 4.5 x^{2} + 12 x - 2

x^{2} y - x y + 3 y^{2}

\frac{6}{x ^{2} + 2}

What is the extreme f(x)=2x^3+6x^2-144x+2,-6<= x<= 5 ?
The extreme f(x)=2x^3+6x^2-144x+2,-6<= x<= 5 is Maximum(-6,650),Minimum(4,-350),Maximum(5,-318)