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

The extreme f(x)=x^3-9x^2+24x-2 is Maximum(2,18),Minimum(4,14)

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

extreme points

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

Maximum (2, 18), Minimum (4, 14)

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 - 2 : 18

Maximum (2, 18)

Plug

x = 4

into

x^{3} - 9 x^{2} + 24 x - 2 : 14

Minimum (4, 14)

Maximum (2, 18), Minimum (4, 14)

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 7 x + 11 y

f (x) = x^{4} - 5 x^{2}

f (x) = 2 x^{2} - 8 x + y^{2} + 16 y + 100

f (x, y) = 2 x^{3} + 9 x y^{2} + 15 x^{2} + 27 y^{2}

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

What is the extreme f(x)=x^3-9x^2+24x-2 ?
The extreme f(x)=x^3-9x^2+24x-2 is Maximum(2,18),Minimum(4,14)