Algebra
Calculus
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Question
Function
Evaluate the derivative
Find the domain
Find the x-intercept/zero
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f′(x)=x2(x−2)2−3x2+4x−4
Evaluate
f(x)=x1+x−22
Take the derivative of both sides
f′(x)=dxd(x1+x−22)
Use differentiation rule dxd(f(x)±g(x))=dxd(f(x))±dxd(g(x))
f′(x)=dxd(x1)+dxd(x−22)
Calculate
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Calculate
dxd(x1)
Rewrite the expression in exponential form
dxd(x−1)
Use dxdxn=nxn−1 to find derivative
−x−2
Express with a positive exponent using a−n=an1
−x21
f′(x)=−x21+dxd(x−22)
Calculate
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Calculate
dxd(x−22)
Use differentiation rules
2×dxd(x−21)
Rewrite the expression in exponential form
2×dxd((x−2)−1)
Calculate the derivative
2(−(x−2)21)
Multiply the terms
−(x−2)22
f′(x)=−x21−(x−2)22
Solution
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Evaluate
−x21−(x−2)22
Reduce fractions to a common denominator
−x2(x−2)2(x−2)2−(x−2)2x22x2
Rewrite the expression
−x2(x−2)2(x−2)2−x2(x−2)22x2
Write all numerators above the common denominator
x2(x−2)2−(x−2)2−2x2
Expand the expression
x2(x−2)2−(x2−4x+4)−2x2
Subtract the terms
x2(x−2)2−3x2+4x−4
f′(x)=x2(x−2)2−3x2+4x−4
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
f(x)=x1+x−22
Rewrite the function using the appropriate notation
y=x1+x−22
To test if the graph of y=x1+x−22 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=−x1+−x−22
Simplify
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Evaluate
−x1+−x−22
Use b−a=−ba=−ba to rewrite the fraction
−x1+−x−22
Use b−a=−ba=−ba to rewrite the fraction
−x1−x+22
Reduce fractions to a common denominator
−x(x+2)x+2−(x+2)x2x
Rewrite the expression
−x(x+2)x+2−x(x+2)2x
Write all numerators above the common denominator
x(x+2)−(x+2)−2x
Subtract the terms
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Evaluate
−(x+2)−2x
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−x−2−2x
Subtract the terms
−3x−2
x(x+2)−3x−2
Use b−a=−ba=−ba to rewrite the fraction
−x(x+2)3x+2
−y=−x(x+2)3x+2
Change the signs both sides
y=x(x+2)3x+2
Solution
Not symmetry with respect to the origin
Show Solution
Graph
