What is the extreme x^3-9x^2+24x-12 ?

The extreme x^3-9x^2+24x-12 is Maximum(2,8),Minimum(4,4)

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extreme x^3-9x^2+24x-12

extreme

Maximum (2, 8), Minimum (4, 4)

Solution steps

f^{'} (x) = 3 x^{2} - 18 x + 24

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 2

into

x^{3} - 9 x^{2} + 24 x - 12 : 8

Maximum (2, 8)

Plug

x = 4

into

x^{3} - 9 x^{2} + 24 x - 12 : 4

Minimum (4, 4)

Maximum (2, 8), Minimum (4, 4)

What is the extreme x^3-9x^2+24x-12 ?
The extreme x^3-9x^2+24x-12 is Maximum(2,8),Minimum(4,4)