What is the extreme f(x)=x^3-6x^2+9x+6 ?

The extreme f(x)=x^3-6x^2+9x+6 is Maximum(1,10),Minimum(3,6)

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extreme f(x)=x^3-6x^2+9x+6

extreme points

f (x) = x^{3} - 6 x^{2} + 9 x + 6

Maximum (1, 10), Minimum (3, 6)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

x^{3} - 6 x^{2} + 9 x + 6 : 10

Maximum (1, 10)

Plug

x = 3

into

x^{3} - 6 x^{2} + 9 x + 6 : 6

Minimum (3, 6)

Maximum (1, 10), Minimum (3, 6)

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

f (x) = 2 x^{2} (ln (x))

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

f (x) = x^{\frac{2}{3}} (x + 2)

y

What is the extreme f(x)=x^3-6x^2+9x+6 ?
The extreme f(x)=x^3-6x^2+9x+6 is Maximum(1,10),Minimum(3,6)