What is the extreme 2x^3+3x^2-36x+3,-3<= x<= 6 ?

The extreme 2x^3+3x^2-36x+3,-3<= x<= 6 is Maximum(-3,84),Minimum(2,-41),Maximum(6,327)

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extreme 2x^3+3x^2-36x+3,-3<= x<= 6

extreme points

2 x^{3} + 3 x^{2} - 36 x + 3, - 3 \leq x \leq 6

Maximum (- 3, 84), Minimum (2, - 41), Maximum (6, 327)

Solution steps

Find the critical points:

x = - 3, x = 2, x = 6

Domain of

2 x^{3} + 3 x^{2} - 36 x + 3, - 3 \leq x \leq 6 : - 3 \leq x \leq 6

Find intervals:

Decreasing

: - 3 < x < 2,

Increasing

: 2 < x < 6

Plug the extreme point

x = - 3

into

2 x^{3} + 3 x^{2} - 36 x + 3 \Rightarrow y = 84

Maximum (- 3, 84)

Plug the extreme point

x = 2

into

2 x^{3} + 3 x^{2} - 36 x + 3 \Rightarrow y = - 41

Minimum (2, - 41)

Plug the extreme point

x = 6

into

2 x^{3} + 3 x^{2} - 36 x + 3 \Rightarrow y = 327

Maximum (6, 327)

Maximum (- 3, 84), Minimum (2, - 41), Maximum (6, 327)

x^{2} + 6 x + 3

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

\frac{2 x + 8}{x ^{2} + 8}

g (t) = - 5 t^{2} - 3 t + 2

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

What is the extreme 2x^3+3x^2-36x+3,-3<= x<= 6 ?
The extreme 2x^3+3x^2-36x+3,-3<= x<= 6 is Maximum(-3,84),Minimum(2,-41),Maximum(6,327)