What is the tangent of 2x^3-x^2+3 ?

The tangent of 2x^3-x^2+3 is y=(6a_{0}^2-2a_{0})x-4a_{0}^3+a_{0}^2+3

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tangent of 2x^3-x^2+3

tangent of

2 x^{3} - x^{2} + 3

y = (6 a_{0}^{2} - 2 a_{0}) x - 4 a_{0}^{3} + a_{0}^{2} + 3

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{3} - a_{0}^{2} + 3)

Find the slope of

y = 2 x^{3} - x^{2} + 3 : \frac{d y}{d x} = 6 x^{2} - 2 x

Compute the slope of

y = 2 x^{3} - x^{2} + 3

x = a_{0} : m = 6 a_{0}^{2} - 2 a_{0}

Find the line with slope m=

6 a_{0}^{2} - 2 a_{0}

and passing through

(a_{0}, 2 a_{0}^{3} - a_{0}^{2} + 3) : y = (6 a_{0}^{2} - 2 a_{0}) x - 4 a_{0}^{3} + a_{0}^{2} + 3

y = (6 a_{0}^{2} - 2 a_{0}) x - 4 a_{0}^{3} + a_{0}^{2} + 3

\frac{d}{d y} (ln (x^{2} + y^{2}))

\frac{d y}{d x} = (x + y + 9)^{2}

\int_{- 2}^{3} \frac{25}{x ^{4}} d x

\int_{0}^{\infty} sin (4 x) d x

What is the tangent of 2x^3-x^2+3 ?
The tangent of 2x^3-x^2+3 is y=(6a_{0}^2-2a_{0})x-4a_{0}^3+a_{0}^2+3