What is the extreme f(x)=x^3-9x^2+24x-18 ?

The extreme f(x)=x^3-9x^2+24x-18 is Maximum(2,2),Minimum(4,-2)

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extreme f(x)=x^3-9x^2+24x-18

extreme points

f (x) = x^{3} - 9 x^{2} + 24 x - 18

Maximum (2, 2), Minimum (4, - 2)

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 - 18 : 2

Maximum (2, 2)

Plug

x = 4

into

x^{3} - 9 x^{2} + 24 x - 18 : - 2

Minimum (4, - 2)

Maximum (2, 2), Minimum (4, - 2)

f (x) = 4 x - 3 x^{2} + 1

g (x, y) = (x^{2} - 1) (e^{y} - 1) + (y^{2} - 2 y + 2) e^{y}

y = (x + 7) (x + 3)

f (x) = - 3 x^{2} + 2 x - 4, 1 \leq x \leq 4

R (M) = M^{2} (\frac{1}{2} - \frac{M}{3})

What is the extreme f(x)=x^3-9x^2+24x-18 ?
The extreme f(x)=x^3-9x^2+24x-18 is Maximum(2,2),Minimum(4,-2)