What is the extreme f(x)=x^3-9x^2+24x+1 ?

The extreme f(x)=x^3-9x^2+24x+1 is Maximum(2,21),Minimum(4,17)

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extreme f(x)=x^3-9x^2+24x+1

extreme points

f (x) = x^{3} - 9 x^{2} + 24 x + 1

Maximum (2, 21), Minimum (4, 17)

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 + 1 : 21

Maximum (2, 21)

Plug

x = 4

into

x^{3} - 9 x^{2} + 24 x + 1 : 17

Minimum (4, 17)

Maximum (2, 21), Minimum (4, 17)

What is the extreme f(x)=x^3-9x^2+24x+1 ?
The extreme f(x)=x^3-9x^2+24x+1 is Maximum(2,21),Minimum(4,17)