Solve -4x^4 - 2x^2 - 3x 7 = y

Function

Find the x -intercept/zero

Find the y-intercept

x_{1} \approx - 1.642221, x_{2} = 0

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y = - 4 x^{4} - 2 x^{2} - 21 x

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Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

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Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = - 16 x^{3} - 4 x - 21

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Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = - 48 x^{2} - 4

Calculate

- 4 x^{4} - 2 x^{2} - 3 x 7 = y

Simplify the expression

- 4 x^{4} - 2 x^{2} - 21 x = y

Take the derivative of both sides

\frac{d}{d x} (- 4 x^{4} - 2 x^{2} - 21 x) = \frac{d}{d x} (y)

Calculate the derivative

More Steps

- 16 x^{3} - 4 x - 21 = \frac{d}{d x} (y)

Calculate the derivative

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- 16 x^{3} - 4 x - 21 = \frac{d y}{d x}

Swap the sides of the equation

\frac{d y}{d x} = - 16 x^{3} - 4 x - 21

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- 16 x^{3} - 4 x - 21)

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- 16 x^{3} - 4 x - 21)

Use differentiation rules

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- 16 x^{3}) + \frac{d}{d x} (- 4 x) + \frac{d}{d x} (- 21)

Evaluate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = - 48 x^{2} + \frac{d}{d x} (- 4 x) + \frac{d}{d x} (- 21)

Evaluate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = - 48 x^{2} - 4 + \frac{d}{d x} (- 21)

Use \frac{d}{d x} (c) = 0 to find derivative

\frac{d ^{2} y}{d x ^{2}} = - 48 x^{2} - 4 + 0

Solution

\frac{d ^{2} y}{d x ^{2}} = - 48 x^{2} - 4

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