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

The extreme f(x)=3x^3-2x^2+6 is Maximum(0,6),Minimum(4/9 , 1426/243)

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

extreme points

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

Maximum (0, 6), Minimum (\frac{4}{9}, \frac{1426}{243})

Solution steps

f^{'} (x) = 9 x^{2} - 4 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{4}{9},

Increasing

: \frac{4}{9} < x < \infty

Plug

x = 0

into

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

Maximum (0, 6)

Plug

x = \frac{4}{9}

into

3 x^{3} - 2 x^{2} + 6 : \frac{1426}{243}

Minimum (\frac{4}{9}, \frac{1426}{243})

Maximum (0, 6), Minimum (\frac{4}{9}, \frac{1426}{243})

K (a, b) = 4 a + 9 ab

e^{- 2.5 x^{2}}

f (x) = - 2 x^{3} + 18 x^{2} - 48 x + 19

f (x) = x^{2} - 1

f (x) = sin (4 x)

What is the extreme f(x)=3x^3-2x^2+6 ?
The extreme f(x)=3x^3-2x^2+6 is Maximum(0,6),Minimum(4/9 , 1426/243)