Solve y=x^210x^27

Question

Function

Evaluate the derivative

Find the domain

Find the x -intercept/zero

y^{'} = 280 x^{3}

Evaluate

y = x^{2} \times 10 x^{2} \times 7

Simplify

More Steps

Evaluate

x^{2} \times 10 x^{2} \times 7

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 10 \times 7

Add the numbers

x^{4} \times 10 \times 7

Multiply the terms

x^{4} \times 70

Use the commutative property to reorder the terms

70 x^{4}

y = 70 x^{4}

Take the derivative of both sides

y^{'} = \frac{d}{d x} (70 x^{4})

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

y^{'} = 70 \times \frac{d}{d x} (x^{4})

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

y^{'} = 70 \times 4 x^{3}

Solution

y^{'} = 280 x^{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

y = x^{2} 10 x^{2} 7

Simplify the expression

y = 70 x^{4}

To test if the graph of y = 70 x^{4} is symmetry with respect to the origin,substitute -x for x and -y for y

- y = 70 (- x)^{4}

Simplify

- y = 70 x^{4}

Change the signs both sides

y = - 70 x^{4}

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{4 7 0 ^{3} y}{70} x = - \frac{4 7 0 ^{3} y}{70}

Evaluate

y = x^{2} \times 10 x^{2} \times 7

Simplify

More Steps

Evaluate

x^{2} \times 10 x^{2} \times 7

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 10 \times 7

Add the numbers

x^{4} \times 10 \times 7

Multiply the terms

x^{4} \times 70

Use the commutative property to reorder the terms

70 x^{4}

y = 70 x^{4}

Swap the sides of the equation

70 x^{4} = y

Divide both sides

\frac{70 x ^{4}}{70} = \frac{y}{70}

Divide the numbers

x^{4} = \frac{y}{70}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{y}{70}

Simplify the expression

More Steps

Evaluate

4 \frac{y}{70}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 y}{4 70}

Multiply by the Conjugate

\frac{4 y \times 4 7 0 ^{3}}{4 70 \times 4 7 0 ^{3}}

Calculate

\frac{4 y \times 4 7 0 ^{3}}{70}

Calculate

More Steps

Evaluate

4 y \times 4 7 0^{3}

The product of roots with the same index is equal to the root of the product

4 y \times 7 0^{3}

Calculate the product

4 7 0^{3} y

\frac{4 7 0 ^{3} y}{70}

x = \pm \frac{4 7 0 ^{3} y}{70}

Solution

x = \frac{4 7 0 ^{3} y}{70} x = - \frac{4 7 0 ^{3} y}{70}

Show Solution

Rewrite the equation

r = 0 r = \frac{3 sin ( θ )}{3 70 cos ( θ ) \times cos ( θ )}

Evaluate

y = x^{2} \times 10 x^{2} \times 7

Simplify

More Steps

Evaluate

x^{2} \times 10 x^{2} \times 7

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 10 \times 7

Add the numbers

x^{4} \times 10 \times 7

Multiply the terms

x^{4} \times 70

Use the commutative property to reorder the terms

70 x^{4}

y = 70 x^{4}

Move the expression to the left side

y - 70 x^{4} = 0

To convert the equation to polar coordinates,substitute x for r cos (θ) and y for r sin (θ)

sin (θ) \times r - 70 (cos (θ) \times r)^{4} = 0

Factor the expression

- 70 cos^{4} (θ) \times r^{4} + sin (θ) \times r = 0

Factor the expression

r (- 70 cos^{4} (θ) \times r^{3} + sin (θ)) = 0

When the product of factors equals 0,at least one factor is 0

r = 0 - 70 cos^{4} (θ) \times r^{3} + sin (θ) = 0

Solution

More Steps

Factor the expression

- 70 cos^{4} (θ) \times r^{3} + sin (θ) = 0

Subtract the terms

- 70 cos^{4} (θ) \times r^{3} + sin (θ) - sin (θ) = 0 - sin (θ)

Evaluate

- 70 cos^{4} (θ) \times r^{3} = - sin (θ)

Divide the terms

r^{3} = \frac{sin ( θ )}{70 cos ^{4} ( θ )}

Simplify the expression

More Steps

Evaluate

3 \frac{sin ( θ )}{70 cos ^{4} ( θ )}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 sin ( θ )}{3 70 cos ^{4} ( θ )}

Simplify the radical expression

\frac{3 sin ( θ )}{3 70 cos ( θ ) \times cos ( θ )}

r = \frac{3 sin ( θ )}{3 70 cos ( θ ) \times cos ( θ )}

r = 0 r = \frac{3 sin ( θ )}{3 70 cos ( θ ) \times cos ( θ )}

Show Solution

Function

Testing for symmetry

Solve the equation

Rewrite the equation

Graph