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

Compute the slope of

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

x = a_{0} : 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

\int_{- 1}^{1} e^{x} - (x^{2} - 2) d x

\frac{\partial}{\partial x} (\frac{2 x - y}{x + 2 y})

\frac{\partial ^{2}}{\partial x ^{2}} (x^{2} - y^{2})

\frac{\partial}{\partial x} ((4 - x^{2} - y^{2})^{\frac{1}{2}})

\frac{d}{d t} (\frac{1}{t ^{2} - 2})

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