What is the inflection f(x)=x^4-7x^3 ?

The inflection f(x)=x^4-7x^3 is (0,0),(7/2 ,-2401/16)

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inflection f(x)=x^4-7x^3

inflection points

f (x) = x^{4} - 7 x^{3}

(0, 0), (\frac{7}{2}, - \frac{2401}{16})

Solution steps

f^{''} (x) = 12 x^{2} - 42 x

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

: 0 < x < \frac{7}{2},

Concave Upward

: \frac{7}{2} < x < \infty

Plug

x = 0

into

x^{4} - 7 x^{3} : 0

(0, 0)

Plug

x = \frac{7}{2}

into

x^{4} - 7 x^{3} : - \frac{2401}{16}

(\frac{7}{2}, - \frac{2401}{16})

(0, 0), (\frac{7}{2}, - \frac{2401}{16})

cos (3 x)

f (x) = 5 cos (x)

f (x) = x^{4} - 8 x^{2}

f (x) = x^{2} - 6 x + 1

f (x) = x^{2} - x - 20

What is the inflection f(x)=x^4-7x^3 ?
The inflection f(x)=x^4-7x^3 is (0,0),(7/2 ,-2401/16)