What is the inflection f(x)=-2/5 x^6+5x^4 ?

The inflection f(x)=-2/5 x^6+5x^4 is (-sqrt(5),75),(sqrt(5),75)

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inflection f(x)=-2/5 x^6+5x^4

inflection points

f (x) = - \frac{2}{5} x^{6} + 5 x^{4}

(- 5, 75), (5, 75)

Solution steps

f^{''} (x) = - 12 x^{4} + 60 x^{2}

Find intervals:

Concave Downward

: - \infty < x < - 5,

Concave Upward

: - 5 < x < 0,

Concave Upward

: 0 < x < 5,

Concave Downward

: 5 < x < \infty

Plug

x = - 5

into

- \frac{2}{5} x^{6} + 5 x^{4} : 75

(- 5, 75)

Plug

x = 5

into

- \frac{2}{5} x^{6} + 5 x^{4} : 75

(5, 75)

(- 5, 75), (5, 75)

What is the inflection f(x)=-2/5 x^6+5x^4 ?
The inflection f(x)=-2/5 x^6+5x^4 is (-sqrt(5),75),(sqrt(5),75)