What is the tangent of 0.72x^3-4.8x^2+0.6x+7.6 ?

The tangent of 0.72x^3-4.8x^2+0.6x+7.6 is y=(2.16a_{0}^2-9.6a_{0}+0.6)x-1.44a_{0}^3+4.8a_{0}^2+7.6

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tangent of 0.72x^3-4.8x^2+0.6x+7.6

tangent of

0.72 x^{3} - 4.8 x^{2} + 0.6 x + 7.6

y = (2.16 a_{0}^{2} - 9.6 a_{0} + 0.6) x - 1.44 a_{0}^{3} + 4.8 a_{0}^{2} + 7.6

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 0.72 a_{0}^{3} - 4.8 a_{0}^{2} + 0.6 a_{0} + 7.6)

Find the slope of

y = 0.72 x^{3} - 4.8 x^{2} + 0.6 x + 7.6 : \frac{d y}{d x} = 2.16 x^{2} - 9.6 x + 0.6

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 = 2.16 a_{0}^{2} - 9.6 a_{0} + 0.6

Find the line with slope m=

2.16 a_{0}^{2} - 9.6 a_{0} + 0.6

and passing through

(a_{0}, 0.72 a_{0}^{3} - 4.8 a_{0}^{2} + 0.6 a_{0} + 7.6) : y = (2.16 a_{0}^{2} - 9.6 a_{0} + 0.6) x - 1.44 a_{0}^{3} + 4.8 a_{0}^{2} + 7.6

y = (2.16 a_{0}^{2} - 9.6 a_{0} + 0.6) x - 1.44 a_{0}^{3} + 4.8 a_{0}^{2} + 7.6

What is the tangent of 0.72x^3-4.8x^2+0.6x+7.6 ?
The tangent of 0.72x^3-4.8x^2+0.6x+7.6 is y=(2.16a_{0}^2-9.6a_{0}+0.6)x-1.44a_{0}^3+4.8a_{0}^2+7.6