Solve 16 - | y | - 4 x = 0

Solve the equation

Solve for x

Solve for y

x = \frac{16 - ∣ y ∣}{4}

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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} = - \frac{4 ∣ y ∣}{y}

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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}} = 0

Calculate

16 - ∣ y ∣ - 4 x = 0

Take the derivative of both sides

\frac{d}{d x} (16 - ∣ y ∣ - 4 x) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

- \frac{y \frac{d y}{d x} + 4 ∣ y ∣}{∣ y ∣} = \frac{d}{d x} (0)

Calculate the derivative

- \frac{y \frac{d y}{d x} + 4 ∣ y ∣}{∣ y ∣} = 0

Simplify

- y \frac{d y}{d x} - 4 ∣ y ∣ = 0

Move the constant to the right side

- y \frac{d y}{d x} = 0 + 4 ∣ y ∣

Removing 0 doesn't change the value,so remove it from the expression

- y \frac{d y}{d x} = 4 ∣ y ∣

Divide both sides

\frac{- y \frac{d y}{d x}}{- y} = \frac{4 ∣ y ∣}{- y}

Divide the numbers

\frac{d y}{d x} = \frac{4 ∣ y ∣}{- y}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{d y}{d x} = - \frac{4 ∣ y ∣}{y}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- \frac{4 ∣ y ∣}{y})

Calculate the derivative

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

Use differentiation rules

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

Calculate the derivative

More Steps

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

Calculate the derivative

More Steps

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

Calculate

More Steps

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

Calculate

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

Solution

\frac{d ^{2} y}{d x ^{2}} = 0

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