What is the inflection f(x)= 1/2 x^4-4x^3 ?

The inflection f(x)= 1/2 x^4-4x^3 is (0,0),(4,-128)

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inflection f(x)= 1/2 x^4-4x^3

inflection points

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

(0, 0), (4, - 128)

Solution steps

f^{''} (x) = 6 x^{2} - 24 x

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

: 0 < x < 4,

Concave Upward

: 4 < x < \infty

Plug

x = 0

into

\frac{1}{2} x^{4} - 4 x^{3} : 0

(0, 0)

Plug

x = 4

into

\frac{1}{2} x^{4} - 4 x^{3} : - 128

(4, - 128)

(0, 0), (4, - 128)

f (x) = lo g_{3} (2 x)

f (x) = 2 x^{3} + 3 x^{2} - 180 x

2^{x + 2} + 2

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

f (x) = x + 8 - 4

What is the inflection f(x)= 1/2 x^4-4x^3 ?
The inflection f(x)= 1/2 x^4-4x^3 is (0,0),(4,-128)