Solve 3x^4=y - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

x = 0

Evaluate

3 x^{4} = y

To find the x -intercept,set y =0

3 x^{4} = 0

Rewrite the expression

x^{4} = 0

Solution

x = 0

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{4 27 y}{3} x = - \frac{4 27 y}{3}

Evaluate

3 x^{4} = y

Divide both sides

\frac{3 x ^{4}}{3} = \frac{y}{3}

Divide the numbers

x^{4} = \frac{y}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{y}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{y}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 y}{4 3}

Multiply by the Conjugate

\frac{4 y \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Calculate

\frac{4 y \times 4 3 ^{3}}{3}

Calculate

More Steps

Evaluate

4 y \times 4 3^{3}

The product of roots with the same index is equal to the root of the product

4 y \times 3^{3}

Calculate the product

4 3^{3} y

\frac{4 3 ^{3} y}{3}

Calculate

\frac{4 27 y}{3}

x = \pm \frac{4 27 y}{3}

Solution

x = \frac{4 27 y}{3} x = - \frac{4 27 y}{3}

Show Solution

Testing for symmetry

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

Evaluate

3 x^{4} = y

To test if the graph of 3 x^{4} = y is symmetry with respect to the origin,substitute -x for x and -y for y

3 (- x)^{4} = - y

Evaluate

3 x^{4} = - y

Solution

Not symmetry with respect to the origin

Show Solution

Rewrite the equation

r = 0 r = \frac{3 sin ( θ )}{3 3 cos ( θ ) \times cos ( θ )}

Evaluate

3 x^{4} = y

Move the expression to the left side

3 x^{4} - y = 0

To convert the equation to polar coordinates,substitute x for r cos (θ) and y for r sin (θ)

3 (cos (θ) \times r)^{4} - sin (θ) \times r = 0

Factor the expression

3 cos^{4} (θ) \times r^{4} - sin (θ) \times r = 0

Factor the expression

r (3 cos^{4} (θ) \times r^{3} - sin (θ)) = 0

When the product of factors equals 0,at least one factor is 0

r = 0 3 cos^{4} (θ) \times r^{3} - sin (θ) = 0

Solution

More Steps

Factor the expression

3 cos^{4} (θ) \times r^{3} - sin (θ) = 0

Subtract the terms

3 cos^{4} (θ) \times r^{3} - sin (θ) - (- sin (θ)) = 0 - (- sin (θ))

Evaluate

3 cos^{4} (θ) \times r^{3} = sin (θ)

Divide the terms

r^{3} = \frac{sin ( θ )}{3 cos ^{4} ( θ )}

Simplify the expression

More Steps

Evaluate

3 \frac{sin ( θ )}{3 cos ^{4} ( θ )}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 sin ( θ )}{3 3 cos ^{4} ( θ )}

Simplify the radical expression

\frac{3 sin ( θ )}{3 3 cos ( θ ) \times cos ( θ )}

r = \frac{3 sin ( θ )}{3 3 cos ( θ ) \times cos ( θ )}

r = 0 r = \frac{3 sin ( θ )}{3 3 cos ( θ ) \times cos ( θ )}

Show Solution

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = 12 x^{3}

Calculate

3 x^{4} = y

Take the derivative of both sides

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

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 x^{4})

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

3 \times \frac{d}{d x} (x^{4})

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

3 \times 4 x^{3}

Multiply the terms

12 x^{3}

12 x^{3} = \frac{d}{d x} (y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (y)

Use differentiation rules

\frac{d}{d y} (y) \times \frac{d y}{d x}

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

\frac{d y}{d x}

12 x^{3} = \frac{d y}{d x}

Solution

\frac{d y}{d x} = 12 x^{3}

Show Solution

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = 36 x^{2}

Calculate

3 x^{4} = y

Take the derivative of both sides

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

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 x^{4})

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

3 \times \frac{d}{d x} (x^{4})

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

3 \times 4 x^{3}

Multiply the terms

12 x^{3}

12 x^{3} = \frac{d}{d x} (y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (y)

Use differentiation rules

\frac{d}{d y} (y) \times \frac{d y}{d x}

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

\frac{d y}{d x}

12 x^{3} = \frac{d y}{d x}

Swap the sides of the equation

\frac{d y}{d x} = 12 x^{3}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (12 x^{3})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (12 x^{3})

Simplify

\frac{d ^{2} y}{d x ^{2}} = 12 \times \frac{d}{d x} (x^{3})

Rewrite the expression

\frac{d ^{2} y}{d x ^{2}} = 12 \times 3 x^{2}

Solution

\frac{d ^{2} y}{d x ^{2}} = 36 x^{2}

Show Solution

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph