What is the extreme f(x)=2x^3-9x^2+12x-3 ?

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

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extreme f(x)=2x^3-9x^2+12x-3

extreme points

f (x) = 2 x^{3} - 9 x^{2} + 12 x - 3

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

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 - 3 : 2

Maximum (1, 2)

Plug

x = 2

into

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

Minimum (2, 1)

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

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