Question
Function
Find the x-intercept/zero
Find the y-intercept
x=0
Evaluate
2x3=y
To find the x-intercept,set y=0
2x3=0
Rewrite the expression
x3=0
Solution
x=0
Show Solution

Solve the equation
Solve for x
Solve for y
x=234y
Evaluate
2x3=y
Divide both sides
22x3=2y
Divide the numbers
x3=2y
Take the 3-th root on both sides of the equation
3x3=32y
Calculate
x=32y
Solution
More Steps

Evaluate
32y
To take a root of a fraction,take the root of the numerator and denominator separately
323y
Multiply by the Conjugate
32×3223y×322
Calculate
23y×322
Calculate
More Steps

Evaluate
3y×322
The product of roots with the same index is equal to the root of the product
3y×22
Calculate the product
322y
2322y
Calculate
234y
x=234y
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
Symmetry with respect to the origin
Evaluate
2x3=y
To test if the graph of 2x3=y is symmetry with respect to the origin,substitute -x for x and -y for y
2(−x)3=−y
Evaluate
More Steps

Evaluate
2(−x)3
Rewrite the expression
2(−x3)
Multiply the numbers
−2x3
−2x3=−y
Solution
Symmetry with respect to the origin
Show Solution

Rewrite the equation
r=0r=2cos3(θ)sin(θ)r=−2cos3(θ)sin(θ)
Evaluate
2x3=y
Move the expression to the left side
2x3−y=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
2(cos(θ)×r)3−sin(θ)×r=0
Factor the expression
2cos3(θ)×r3−sin(θ)×r=0
Factor the expression
r(2cos3(θ)×r2−sin(θ))=0
When the product of factors equals 0,at least one factor is 0
r=02cos3(θ)×r2−sin(θ)=0
Solution
More Steps

Factor the expression
2cos3(θ)×r2−sin(θ)=0
Subtract the terms
2cos3(θ)×r2−sin(θ)−(−sin(θ))=0−(−sin(θ))
Evaluate
2cos3(θ)×r2=sin(θ)
Divide the terms
r2=2cos3(θ)sin(θ)
Evaluate the power
r=±2cos3(θ)sin(θ)
Separate into possible cases
r=2cos3(θ)sin(θ)r=−2cos3(θ)sin(θ)
r=0r=2cos3(θ)sin(θ)r=−2cos3(θ)sin(θ)
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=6x2
Calculate
2x3=y
Take the derivative of both sides
dxd(2x3)=dxd(y)
Calculate the derivative
More Steps

Evaluate
dxd(2x3)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
2×dxd(x3)
Use dxdxn=nxn−1 to find derivative
2×3x2
Multiply the terms
6x2
6x2=dxd(y)
Calculate the derivative
More Steps

Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
6x2=dxdy
Solution
dxdy=6x2
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=12x
Calculate
2x3=y
Take the derivative of both sides
dxd(2x3)=dxd(y)
Calculate the derivative
More Steps

Evaluate
dxd(2x3)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
2×dxd(x3)
Use dxdxn=nxn−1 to find derivative
2×3x2
Multiply the terms
6x2
6x2=dxd(y)
Calculate the derivative
More Steps

Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
6x2=dxdy
Swap the sides of the equation
dxdy=6x2
Take the derivative of both sides
dxd(dxdy)=dxd(6x2)
Calculate the derivative
dx2d2y=dxd(6x2)
Simplify
dx2d2y=6×dxd(x2)
Rewrite the expression
dx2d2y=6×2x
Solution
dx2d2y=12x
Show Solution
