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

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

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tangent of 2x^2-x^4

tangent of

2 x^{2} - x^{4}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = 2 x^{2} - x^{4} : \frac{d y}{d x} = 4 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 = 4 a_{0} - 4 a_{0}^{3}

Find the line with slope m=

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

and passing through

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

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

x \to - 3 lim (\frac{7}{( x + 3 ) ^{2}})

f (x) = \frac{3}{x}, at x = 2

\frac{\partial}{\partial x} (ln (7 x^{2} + 4 y^{2} + 8))

y^{2} - 3 x = 4, x - y = 2

y = \frac{2}{x} - \frac{x}{2}

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