What is the extreme f(1)=x^3-6x^2+9x+2 ?

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

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extreme f(1)=x^3-6x^2+9x+2

extreme points

f (1) = x^{3} - 6 x^{2} + 9 x + 2

Maximum (1, 6), Minimum (3, 2)

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 + 2 : 6

Maximum (1, 6)

Plug

x = 3

into

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

Minimum (3, 2)

Maximum (1, 6), Minimum (3, 2)

f (x) = \frac{2}{3} x^{3} + \frac{11}{2} x^{2} - 21 x + 5

f (x) = (x - 3) e^{- 5 x}

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

g (x) = e^{- x^{4}}, - 3 \leq x \leq 1

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

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