What is the inflection f(x)=3x^4-4x^3+2 ?

The inflection f(x)=3x^4-4x^3+2 is (0,2),(2/3 , 38/27)

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inflection f(x)=3x^4-4x^3+2

inflection points

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

(0, 2), (\frac{2}{3}, \frac{38}{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} + 2 : 2

(0, 2)

Plug

x = \frac{2}{3}

into

3 x^{4} - 4 x^{3} + 2 : \frac{38}{27}

(\frac{2}{3}, \frac{38}{27})

(0, 2), (\frac{2}{3}, \frac{38}{27})

What is the inflection f(x)=3x^4-4x^3+2 ?
The inflection f(x)=3x^4-4x^3+2 is (0,2),(2/3 , 38/27)