Question
Function
Evaluate the derivative
Find the domain
Find the x-intercept/zero
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y′=2x−168x3
Evaluate
y=x2−7x4×6
Simplify
y=x2−42x4
Take the derivative of both sides
y′=dxd(x2−42x4)
Use differentiation rule dxd(f(x)±g(x))=dxd(f(x))±dxd(g(x))
y′=dxd(x2)−dxd(42x4)
Use dxdxn=nxn−1 to find derivative
y′=2x−dxd(42x4)
Solution
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Calculate
dxd(42x4)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
42×dxd(x4)
Use dxdxn=nxn−1 to find derivative
42×4x3
Multiply the terms
168x3
y′=2x−168x3
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
y=x2−7x46
Simplify the expression
y=x2−42x4
To test if the graph of y=x2−42x4 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=(−x)2−42(−x)4
Simplify
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Evaluate
(−x)2−42(−x)4
Multiply the terms
(−x)2−42x4
Rewrite the expression
x2−42x4
−y=x2−42x4
Change the signs both sides
y=−x2+42x4
Solution
Not symmetry with respect to the origin
Show Solution

Solve the equation
Solve for x
Solve for y
x=4221+211−168yx=−4221+211−168yx=4221−211−168yx=−4221−211−168y
Evaluate
y=x2−7x4×6
Simplify
y=x2−42x4
Swap the sides of the equation
x2−42x4=y
Move the expression to the left side
x2−42x4−y=0
Solve the equation using substitution t=x2
t−42t2−y=0
Rewrite in standard form
−42t2+t−y=0
Multiply both sides
42t2−t+y=0
Substitute a=42,b=−1 and c=y into the quadratic formula t=2a−b±b2−4ac
t=2×421±(−1)2−4×42y
Simplify the expression
t=841±(−1)2−4×42y
Simplify the expression
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Evaluate
(−1)2−4×42y
Evaluate the power
1−4×42y
Multiply the terms
1−168y
t=841±1−168y
Separate the equation into 2 possible cases
t=841+1−168yt=841−1−168y
Substitute back
x2=841+1−168yx2=841−1−168y
Solve the equation for x
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Substitute back
x2=841+1−168y
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±841+1−168y
Simplify the expression
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Evaluate
841+1−168y
To take a root of a fraction,take the root of the numerator and denominator separately
841+1−168y
Simplify the radical expression
2211+1−168y
Multiply by the Conjugate
221×211+1−168y×21
Calculate
2×211+1−168y×21
Calculate
2×2121+211−168y
Calculate
4221+211−168y
x=±4221+211−168y
Separate the equation into 2 possible cases
x=4221+211−168yx=−4221+211−168y
x=4221+211−168yx=−4221+211−168yx2=841−1−168y
Solution
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Substitute back
x2=841−1−168y
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±841−1−168y
Simplify the expression
More Steps

Evaluate
841−1−168y
To take a root of a fraction,take the root of the numerator and denominator separately
841−1−168y
Simplify the radical expression
2211−1−168y
Multiply by the Conjugate
221×211−1−168y×21
Calculate
2×211−1−168y×21
Calculate
2×2121−211−168y
Calculate
4221−211−168y
x=±4221−211−168y
Separate the equation into 2 possible cases
x=4221−211−168yx=−4221−211−168y
x=4221+211−168yx=−4221+211−168yx=4221−211−168yx=−4221−211−168y
Show Solution
