Question
Function
Evaluate the derivative
Find the domain
Find the x-intercept/zero
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y′=280x3
Evaluate
y=x2×10x2×7
Simplify
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Evaluate
x2×10x2×7
Multiply the terms with the same base by adding their exponents
x2+2×10×7
Add the numbers
x4×10×7
Multiply the terms
x4×70
Use the commutative property to reorder the terms
70x4
y=70x4
Take the derivative of both sides
y′=dxd(70x4)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
y′=70×dxd(x4)
Use dxdxn=nxn−1 to find derivative
y′=70×4x3
Solution
y′=280x3
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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
y=x210x27
Simplify the expression
y=70x4
To test if the graph of y=70x4 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=70(−x)4
Simplify
−y=70x4
Change the signs both sides
y=−70x4
Solution
Not symmetry with respect to the origin
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Solve the equation
Solve for x
Solve for y
x=704703yx=−704703y
Evaluate
y=x2×10x2×7
Simplify
More Steps

Evaluate
x2×10x2×7
Multiply the terms with the same base by adding their exponents
x2+2×10×7
Add the numbers
x4×10×7
Multiply the terms
x4×70
Use the commutative property to reorder the terms
70x4
y=70x4
Swap the sides of the equation
70x4=y
Divide both sides
7070x4=70y
Divide the numbers
x4=70y
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±470y
Simplify the expression
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Evaluate
470y
To take a root of a fraction,take the root of the numerator and denominator separately
4704y
Multiply by the Conjugate
470×47034y×4703
Calculate
704y×4703
Calculate
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Evaluate
4y×4703
The product of roots with the same index is equal to the root of the product
4y×703
Calculate the product
4703y
704703y
x=±704703y
Solution
x=704703yx=−704703y
Show Solution

Rewrite the equation
r=0r=370cos(θ)×cos(θ)3sin(θ)
Evaluate
y=x2×10x2×7
Simplify
More Steps

Evaluate
x2×10x2×7
Multiply the terms with the same base by adding their exponents
x2+2×10×7
Add the numbers
x4×10×7
Multiply the terms
x4×70
Use the commutative property to reorder the terms
70x4
y=70x4
Move the expression to the left side
y−70x4=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
sin(θ)×r−70(cos(θ)×r)4=0
Factor the expression
−70cos4(θ)×r4+sin(θ)×r=0
Factor the expression
r(−70cos4(θ)×r3+sin(θ))=0
When the product of factors equals 0,at least one factor is 0
r=0−70cos4(θ)×r3+sin(θ)=0
Solution
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Factor the expression
−70cos4(θ)×r3+sin(θ)=0
Subtract the terms
−70cos4(θ)×r3+sin(θ)−sin(θ)=0−sin(θ)
Evaluate
−70cos4(θ)×r3=−sin(θ)
Divide the terms
r3=70cos4(θ)sin(θ)
Simplify the expression
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Evaluate
370cos4(θ)sin(θ)
To take a root of a fraction,take the root of the numerator and denominator separately
370cos4(θ)3sin(θ)
Simplify the radical expression
370cos(θ)×cos(θ)3sin(θ)
r=370cos(θ)×cos(θ)3sin(θ)
r=0r=370cos(θ)×cos(θ)3sin(θ)
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