What is the extreme f(x)=x^3-12x^2+45x+1 ?

The extreme f(x)=x^3-12x^2+45x+1 is Maximum(3,55),Minimum(5,51)

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extreme f(x)=x^3-12x^2+45x+1

extreme points

f (x) = x^{3} - 12 x^{2} + 45 x + 1

Maximum (3, 55), Minimum (5, 51)

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 + 1 : 55

Maximum (3, 55)

Plug

x = 5

into

x^{3} - 12 x^{2} + 45 x + 1 : 51

Minimum (5, 51)

Maximum (3, 55), Minimum (5, 51)

What is the extreme f(x)=x^3-12x^2+45x+1 ?
The extreme f(x)=x^3-12x^2+45x+1 is Maximum(3,55),Minimum(5,51)