Solve y=x^2-7x^46

Question

Function

Evaluate the derivative

Find the domain

Find the x -intercept/zero

y^{'} = 2 x - 168 x^{3}

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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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Solve for x

Solve for y

x = \frac{21 + 21 1 - 168 y}{42} x = - \frac{21 + 21 1 - 168 y}{42} x = \frac{21 - 21 1 - 168 y}{42} x = - \frac{21 - 21 1 - 168 y}{42}

Evaluate

y = x^{2} - 7 x^{4} \times 6

Simplify

y = x^{2} - 42 x^{4}

Swap the sides of the equation

x^{2} - 42 x^{4} = y

Move the expression to the left side

x^{2} - 42 x^{4} - y = 0

Solve the equation using substitution t = x^{2}

t - 42 t^{2} - y = 0

Rewrite in standard form

- 42 t^{2} + t - y = 0

Multiply both sides

42 t^{2} - t + y = 0

Substitute a= 42,b= - 1 and c= y into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 42 y}{2 \times 42}

Simplify the expression

t = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 42 y}{84}

Simplify the expression

More Steps

t = \frac{1 \pm 1 - 168 y}{84}

Separate the equation into 2 possible cases

t = \frac{1 + 1 - 168 y}{84} t = \frac{1 - 1 - 168 y}{84}

Substitute back

x^{2} = \frac{1 + 1 - 168 y}{84} x^{2} = \frac{1 - 1 - 168 y}{84}

Solve the equation for x

More Steps

x = \frac{21 + 21 1 - 168 y}{42} x = - \frac{21 + 21 1 - 168 y}{42} x^{2} = \frac{1 - 1 - 168 y}{84}

Solution

More Steps

x = \frac{21 + 21 1 - 168 y}{42} x = - \frac{21 + 21 1 - 168 y}{42} x = \frac{21 - 21 1 - 168 y}{42} x = - \frac{21 - 21 1 - 168 y}{42}

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