What is the tangent of x^2-x^4 ?

The tangent of x^2-x^4 is y=(2a_{0}-4a_{0}^3)x+3a_{0}^4-a_{0}^2

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tangent of x^2-x^4

tangent of

x^{2} - x^{4}

y = (2 a_{0} - 4 a_{0}^{3}) x + 3 a_{0}^{4} - a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} - a_{0}^{4})

Find the slope of

y = x^{2} - x^{4} : \frac{d y}{d x} = 2 x - 4 x^{3}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 2 a_{0} - 4 a_{0}^{3}

Find the line with slope m=

2 a_{0} - 4 a_{0}^{3}

and passing through

(a_{0}, a_{0}^{2} - a_{0}^{4}) : y = (2 a_{0} - 4 a_{0}^{3}) x + 3 a_{0}^{4} - a_{0}^{2}

y = (2 a_{0} - 4 a_{0}^{3}) x + 3 a_{0}^{4} - a_{0}^{2}

What is the tangent of x^2-x^4 ?
The tangent of x^2-x^4 is y=(2a_{0}-4a_{0}^3)x+3a_{0}^4-a_{0}^2