What is the extreme 2x^3-27x^2+84x,1<= x<= 8 ?

The extreme 2x^3-27x^2+84x,1<= x<= 8 is Minimum(1,59),Maximum(2,76),Minimum(7,-49),Maximum(8,-32)

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extreme 2x^3-27x^2+84x,1<= x<= 8

extreme points

2 x^{3} - 27 x^{2} + 84 x, 1 \leq x \leq 8

Minimum (1, 59), Maximum (2, 76), Minimum (7, - 49), Maximum (8, - 32)

Solution steps

Find the critical points:

x = 1, x = 2, x = 7, x = 8

Domain of

2 x^{3} - 27 x^{2} + 84 x, 1 \leq x \leq 8 : 1 \leq x \leq 8

Find intervals:

Increasing

: 1 < x < 2,

Decreasing

: 2 < x < 7,

Increasing

: 7 < x < 8

Plug the extreme point

x = 1

into

2 x^{3} - 27 x^{2} + 84 x \Rightarrow y = 59

Minimum (1, 59)

Plug the extreme point

x = 2

into

2 x^{3} - 27 x^{2} + 84 x \Rightarrow y = 76

Maximum (2, 76)

Plug the extreme point

x = 7

into

2 x^{3} - 27 x^{2} + 84 x \Rightarrow y = - 49

Minimum (7, - 49)

Plug the extreme point

x = 8

into

2 x^{3} - 27 x^{2} + 84 x \Rightarrow y = - 32

Maximum (8, - 32)

Minimum (1, 59), Maximum (2, 76), Minimum (7, - 49), Maximum (8, - 32)

f (x, y) = 1 0^{- 4} y - 2 \cdot 1 0^{- 8} y^{2}

f (x) = - 4 x^{2} + 4 x - 3

f (x) = x^{2} lo g_{10} (2 x)

f (x) = - [x + 2]

f (x) = 2 x^{3} + 9 x^{2} - 24 x, - 5 \leq x \leq 2

What is the extreme 2x^3-27x^2+84x,1<= x<= 8 ?
The extreme 2x^3-27x^2+84x,1<= x<= 8 is Minimum(1,59),Maximum(2,76),Minimum(7,-49),Maximum(8,-32)