What is the tangent of 2x^3(2.16) ?

The tangent of 2x^3(2.16) is y=12.96a_{0}^2x-(216a_{0}^3)/(25)

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tangent of 2x^3(2.16)

tangent of

2 x^{3} (2.16)

y = 12.96 a_{0}^{2} x - \frac{216 a _{0}^{3}}{25}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4.32 a_{0}^{3})

Find the slope of

y = 2 x^{3} 2.16 : \frac{d y}{d x} = 12.96 x^{2}

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 = 12.96 a_{0}^{2}

Find the line with slope m=

12.96 a_{0}^{2}

and passing through

(a_{0}, 4.32 a_{0}^{3}) : y = 12.96 a_{0}^{2} x - \frac{216 a _{0}^{3}}{25}

y = 12.96 a_{0}^{2} x - \frac{216 a _{0}^{3}}{25}

What is the tangent of 2x^3(2.16) ?
The tangent of 2x^3(2.16) is y=12.96a_{0}^2x-(216a_{0}^3)/(25)