Solve y=x^3-x^2-6x^2

Function

Evaluate the derivative

Find the domain

Find the x -intercept/zero

y^{'} = 3 x^{2} - 14 x

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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

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y = x^{3} - 7 x^{2}

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r = 0 r = \frac{7 cos ^{2} ( θ ) - cos ( θ ) ( 49 cos ( θ ) + 4 sin ( θ ) ) \times ∣ cos ( θ ) ∣}{2 cos ^{3} ( θ )} r = \frac{7 cos ^{2} ( θ ) + cos ( θ ) ( 49 cos ( θ ) + 4 sin ( θ ) ) \times ∣ cos ( θ ) ∣}{2 cos ^{3} ( θ )}

Evaluate

y = x^{3} - x^{2} - 6 x^{2}

Simplify

More Steps

y = x^{3} - 7 x^{2}

Move the expression to the left side

y - x^{3} + 7 x^{2} = 0

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

sin (θ) \times r - (cos (θ) \times r)^{3} + 7 (cos (θ) \times r)^{2} = 0

Factor the expression

- cos^{3} (θ) \times r^{3} + 7 cos^{2} (θ) \times r^{2} + sin (θ) \times r = 0

Factor the expression

r (- cos^{3} (θ) \times r^{2} + 7 cos^{2} (θ) \times r + sin (θ)) = 0

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

r = 0 - cos^{3} (θ) \times r^{2} + 7 cos^{2} (θ) \times r + sin (θ) = 0

Solution

More Steps

r = 0 r = \frac{7 cos ^{2} ( θ ) - cos ( θ ) ( 49 cos ( θ ) + 4 sin ( θ ) ) \times ∣ cos ( θ ) ∣}{2 cos ^{3} ( θ )} r = \frac{7 cos ^{2} ( θ ) + cos ( θ ) ( 49 cos ( θ ) + 4 sin ( θ ) ) \times ∣ cos ( θ ) ∣}{2 cos ^{3} ( θ )}

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