What is the extreme x^3-12x^2+45x-4 ?

The extreme x^3-12x^2+45x-4 is Maximum(3,50),Minimum(5,46)

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extreme x^3-12x^2+45x-4

extreme

Maximum (3, 50), Minimum (5, 46)

Solution steps

f^{'} (x) = 3 x^{2} - 24 x + 45

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 3

into

x^{3} - 12 x^{2} + 45 x - 4 : 50

Maximum (3, 50)

Plug

x = 5

into

x^{3} - 12 x^{2} + 45 x - 4 : 46

Minimum (5, 46)

Maximum (3, 50), Minimum (5, 46)

What is the extreme x^3-12x^2+45x-4 ?
The extreme x^3-12x^2+45x-4 is Maximum(3,50),Minimum(5,46)