What is the tangent of y=x^2-x^4(1) ?

The tangent of y=x^2-x^4(1) is y=(2a_{0}-4a_{0}^3)x+3a_{0}^4-a_{0}^2

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tangent of y=x^2-x^4(1)

tangent of

y = x^{2} - x^{4} (1)

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} 1 : \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}

\frac{d}{d x} (2 x^{3} + \frac{2}{x ^{3}})

\frac{d y}{d x} = 0.0019 y (1000 - y)

y^{\frac{1}{2}} \frac{d y}{d x} + y^{\frac{3}{2}} = 1, y (0) = 4

y = x^{2} - 8 x

\int \frac{5 + 7 x}{1 + x ^{2}} d x

What is the tangent of y=x^2-x^4(1) ?
The tangent of y=x^2-x^4(1) is y=(2a_{0}-4a_{0}^3)x+3a_{0}^4-a_{0}^2