What is the tangent of 4x-(x^3)/4 ?

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

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tangent of 4x-(x^3)/4

tangent of

4 x - \frac{x ^{3}}{4}

y = (4 - \frac{3 a _{0}^{2}}{4}) x + \frac{a _{0}^{3}}{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4 a_{0} - \frac{a _{0}^{3}}{4})

Find the slope of

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

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 - \frac{3 a _{0}^{2}}{4}

Find the line with slope m=

4 - \frac{3 a _{0}^{2}}{4}

and passing through

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

y = (4 - \frac{3 a _{0}^{2}}{4}) x + \frac{a _{0}^{3}}{2}

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