What is the inflection 3x^5-5x^3 ?

The inflection 3x^5-5x^3 is (-1/(sqrt(2)), 7/(4sqrt(2))),(0,0),(1/(sqrt(2)),-7/(4sqrt(2)))

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inflection 3x^5-5x^3

inflection points

3 x^{5} - 5 x^{3}

(- \frac{1}{2}, \frac{7}{4 2}), (0, 0), (\frac{1}{2}, - \frac{7}{4 2})

Solution steps

f^{''} (x) = 60 x^{3} - 30 x

Find intervals:

Concave Downward

: - \infty < x < - \frac{1}{2},

Concave Upward

: - \frac{1}{2} < x < 0,

Concave Downward

: 0 < x < \frac{1}{2},

Concave Upward

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

3 x^{5} - 5 x^{3} : \frac{7}{4 2}

(- \frac{1}{2}, \frac{7}{4 2})

Plug

x = 0

into

3 x^{5} - 5 x^{3} : 0

(0, 0)

Plug

x = \frac{1}{2}

into

3 x^{5} - 5 x^{3} : - \frac{7}{4 2}

(\frac{1}{2}, - \frac{7}{4 2})

(- \frac{1}{2}, \frac{7}{4 2}), (0, 0), (\frac{1}{2}, - \frac{7}{4 2})

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

(- 4, 3), (- 2, - 5)

f (x) = \frac{- 6}{x + 9}

x + 2 y = 6

f (x) = \frac{x}{1 + x ^{2}}

What is the inflection 3x^5-5x^3 ?
The inflection 3x^5-5x^3 is (-1/(sqrt(2)), 7/(4sqrt(2))),(0,0),(1/(sqrt(2)),-7/(4sqrt(2)))