Question
Function
Evaluate the derivative
Find the domain
Find the x-intercept/zero
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f′(x)=−(x2−x−6)2x2+6x+3
Evaluate
f(x)=x2−x−6x+3
Take the derivative of both sides
f′(x)=dxd(x2−x−6x+3)
Use differentiation rule dxd(g(x)f(x))=(g(x))2dxd(f(x))×g(x)−f(x)×dxd(g(x))
f′(x)=(x2−x−6)2dxd(x+3)×(x2−x−6)−(x+3)×dxd(x2−x−6)
Calculate
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Evaluate
dxd(x+3)
Use differentiation rule dxd(f(x)±g(x))=dxd(f(x))±dxd(g(x))
dxd(x)+dxd(3)
Use dxdxn=nxn−1 to find derivative
1+dxd(3)
Use dxd(c)=0 to find derivative
1+0
Removing 0 doesn't change the value,so remove it from the expression
1
f′(x)=(x2−x−6)21×(x2−x−6)−(x+3)×dxd(x2−x−6)
Calculate
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Evaluate
dxd(x2−x−6)
Use differentiation rule dxd(f(x)±g(x))=dxd(f(x))±dxd(g(x))
dxd(x2)−dxd(x)−dxd(6)
Use dxdxn=nxn−1 to find derivative
2x−dxd(x)−dxd(6)
Use dxdxn=nxn−1 to find derivative
2x−1−dxd(6)
Use dxd(c)=0 to find derivative
2x−1−0
Removing 0 doesn't change the value,so remove it from the expression
2x−1
f′(x)=(x2−x−6)21×(x2−x−6)−(x+3)(2x−1)
Any expression multiplied by 1 remains the same
f′(x)=(x2−x−6)2x2−x−6−(x+3)(2x−1)
Subtract the terms
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Evaluate
x2−x−6−(x+3)(2x−1)
Rewrite the expression
x2−x−6+(−x−3)(2x−1)
Expand the expression
x2−x−6−2x2−5x+3
Subtract the terms
−x2−x−6−5x+3
Subtract the terms
−x2−6x−6+3
Add the numbers
−x2−6x−3
f′(x)=(x2−x−6)2−x2−6x−3
Solution
f′(x)=−(x2−x−6)2x2+6x+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
f(x)=x2−x−6x+3
Rewrite the function using the appropriate notation
y=x2−x−6x+3
To test if the graph of y=x2−x−6x+3 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=(−x)2−(−x)−6−x+3
Simplify
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Evaluate
(−x)2−(−x)−6−x+3
Subtract the terms
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Evaluate
(−x)2−(−x)−6
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+x−6
Rewrite the expression
x2+x−6
x2+x−6−x+3
−y=x2+x−6−x+3
Change the signs both sides
y=−x2+x−6−x+3
Solution
Not symmetry with respect to the origin
Show Solution