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

The extreme f(x)=x^3-9x^2+24x is Maximum(2,20),Minimum(4,16)

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

extreme points

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

Maximum (2, 20), Minimum (4, 16)

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 : 20

Maximum (2, 20)

Plug

x = 4

into

x^{3} - 9 x^{2} + 24 x : 16

Minimum (4, 16)

Maximum (2, 20), Minimum (4, 16)

f (x) = - 2 x^{3} + 3 x^{2} + 12 x - 5

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

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

f (x, y) = x^{4} - 4 x y + 2 y^{2}

f (x, y) = ln (x) y

What is the extreme f(x)=x^3-9x^2+24x ?
The extreme f(x)=x^3-9x^2+24x is Maximum(2,20),Minimum(4,16)