What is the inflection f(x)=3x^4-4x^3+6 ?

The inflection f(x)=3x^4-4x^3+6 is (0,6),(2/3 , 146/27)

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inflection f(x)=3x^4-4x^3+6

inflection points

f (x) = 3 x^{4} - 4 x^{3} + 6

(0, 6), (\frac{2}{3}, \frac{146}{27})

Solution steps

f^{''} (x) = 36 x^{2} - 24 x

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

: 0 < x < \frac{2}{3},

Concave Upward

: \frac{2}{3} < x < \infty

Plug

x = 0

into

3 x^{4} - 4 x^{3} + 6 : 6

(0, 6)

Plug

x = \frac{2}{3}

into

3 x^{4} - 4 x^{3} + 6 : \frac{146}{27}

(\frac{2}{3}, \frac{146}{27})

(0, 6), (\frac{2}{3}, \frac{146}{27})

1 + x

(1, 2), (- 1, 3)

f (x) = x^{3} - 75 x + 3

f (x) = \frac{( x ^{2} - 4 x + 3 )}{x - 1}

y + 4 = (- \frac{7}{8}) (x - 7)

What is the inflection f(x)=3x^4-4x^3+6 ?
The inflection f(x)=3x^4-4x^3+6 is (0,6),(2/3 , 146/27)