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Popular Functions >

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

Solution

inflection points

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

Solution

(0, 0), (\frac{3}{2}, - \frac{81}{16})

Solution steps

f^{''} (x) = 12 x^{2} - 18 x

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

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

Concave Upward

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

Plug

x = 0

into

x^{4} - 3 x^{3} : 0

(0, 0)

Plug

x = \frac{3}{2}

into

x^{4} - 3 x^{3} : - \frac{81}{16}

(\frac{3}{2}, - \frac{81}{16})

(0, 0), (\frac{3}{2}, - \frac{81}{16})

Graph

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Frequently Asked Questions (FAQ)

What is the inflection f(x)=x^4-3x^3 ?
The inflection f(x)=x^4-3x^3 is (0,0),(3/2 ,-81/16)