Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the x-intercept/zero
Find the y-intercept
No x-intercept
Evaluate
2x−8−3x3×x=y×1
To find the x-intercept,set y=0
2x−8−3x3×x=0×1
Any expression multiplied by 0 equals 0
2x−8−3x3×x=0
Multiply
More Steps
Evaluate
−3x3×x
Multiply the terms with the same base by adding their exponents
−3x3+1
Add the numbers
−3x4
2x−8−3x4=0
Calculate
x∈/R
Solution
No x-intercept
Show Solution
Solve the equation
y=2x−8−3x4
Evaluate
2x−8−3x3×x=y×1
Multiply
More Steps
Evaluate
−3x3×x
Multiply the terms with the same base by adding their exponents
−3x3+1
Add the numbers
−3x4
2x−8−3x4=y×1
Any expression multiplied by 1 remains the same
2x−8−3x4=y
Solution
y=2x−8−3x4
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
2x−8−3x3x=y1
Simplify the expression
2x−8−3x4=y
To test if the graph of 2x−8−3x4=y is symmetry with respect to the origin,substitute -x for x and -y for y
2(−x)−8−3(−x)4=−y
Evaluate
More Steps
Evaluate
2(−x)−8−3(−x)4
Multiply the numbers
−2x−8−3(−x)4
Multiply the terms
−2x−8−3x4
−2x−8−3x4=−y
Solution
Not symmetry with respect to the origin
Show Solution
Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=2−12x3
Calculate
2x−8−3x3x=y1
Simplify the expression
2x−8−3x4=y
Take the derivative of both sides
dxd(2x−8−3x4)=dxd(y)
Calculate the derivative
More Steps
Evaluate
dxd(2x−8−3x4)
Use differentiation rules
dxd(2x)+dxd(−8)+dxd(−3x4)
Evaluate the derivative
More Steps
Evaluate
dxd(2x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
2×dxd(x)
Use dxdxn=nxn−1 to find derivative
2×1
Any expression multiplied by 1 remains the same
2
2+dxd(−8)+dxd(−3x4)
Use dxd(c)=0 to find derivative
2+0+dxd(−3x4)
Evaluate the derivative
More Steps
Evaluate
dxd(−3x4)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−3×dxd(x4)
Use dxdxn=nxn−1 to find derivative
−3×4x3
Multiply the terms
−12x3
2+0−12x3
Evaluate
2−12x3
2−12x3=dxd(y)
Calculate the derivative
More Steps
Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
2−12x3=dxdy
Solution
dxdy=2−12x3
Show Solution
Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=−36x2
Calculate
2x−8−3x3x=y1
Simplify the expression
2x−8−3x4=y
Take the derivative of both sides
dxd(2x−8−3x4)=dxd(y)
Calculate the derivative
More Steps
Evaluate
dxd(2x−8−3x4)
Use differentiation rules
dxd(2x)+dxd(−8)+dxd(−3x4)
Evaluate the derivative
More Steps
Evaluate
dxd(2x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
2×dxd(x)
Use dxdxn=nxn−1 to find derivative
2×1
Any expression multiplied by 1 remains the same
2
2+dxd(−8)+dxd(−3x4)
Use dxd(c)=0 to find derivative
2+0+dxd(−3x4)
Evaluate the derivative
More Steps
Evaluate
dxd(−3x4)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−3×dxd(x4)
Use dxdxn=nxn−1 to find derivative
−3×4x3
Multiply the terms
−12x3
2+0−12x3
Evaluate
2−12x3
2−12x3=dxd(y)
Calculate the derivative
More Steps
Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
2−12x3=dxdy
Swap the sides of the equation
dxdy=2−12x3
Take the derivative of both sides
dxd(dxdy)=dxd(2−12x3)
Calculate the derivative
dx2d2y=dxd(2−12x3)
Use differentiation rules
dx2d2y=dxd(2)+dxd(−12x3)
Use dxd(c)=0 to find derivative
dx2d2y=0+dxd(−12x3)
Evaluate the derivative
More Steps
Evaluate
dxd(−12x3)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−12×dxd(x3)
Use dxdxn=nxn−1 to find derivative
−12×3x2
Multiply the terms
−36x2
dx2d2y=0−36x2
Solution
dx2d2y=−36x2
Show Solution
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