What is the extreme f(x)=x^3-12x^2+45x+9 ?

The extreme f(x)=x^3-12x^2+45x+9 is Maximum(3,63),Minimum(5,59)

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extreme f(x)=x^3-12x^2+45x+9

extreme points

f (x) = x^{3} - 12 x^{2} + 45 x + 9

Maximum (3, 63), Minimum (5, 59)

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 + 9 : 63

Maximum (3, 63)

Plug

x = 5

into

x^{3} - 12 x^{2} + 45 x + 9 : 59

Minimum (5, 59)

Maximum (3, 63), Minimum (5, 59)

f (x, y) = x^{- 1} - 64 y^{- 1} + x y

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

x^{2} - y^{2} - 2 x + 4 y + 6

f (x) = ln (4 x^{2} + 18 y^{2} - 36)

f (x) = x^{3} + y^{3} - 15 x y

What is the extreme f(x)=x^3-12x^2+45x+9 ?
The extreme f(x)=x^3-12x^2+45x+9 is Maximum(3,63),Minimum(5,59)