What is the extreme 2x^3-9x^2+12x-6 ?

The extreme 2x^3-9x^2+12x-6 is Maximum(1,-1),Minimum(2,-2)

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extreme 2x^3-9x^2+12x-6

extreme points

2 x^{3} - 9 x^{2} + 12 x - 6

Maximum (1, - 1), Minimum (2, - 2)

Solution steps

f^{'} (x) = 6 x^{2} - 18 x + 12

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 1

into

2 x^{3} - 9 x^{2} + 12 x - 6 : - 1

Maximum (1, - 1)

Plug

x = 2

into

2 x^{3} - 9 x^{2} + 12 x - 6 : - 2

Minimum (2, - 2)

Maximum (1, - 1), Minimum (2, - 2)

What is the extreme 2x^3-9x^2+12x-6 ?
The extreme 2x^3-9x^2+12x-6 is Maximum(1,-1),Minimum(2,-2)