What is the tangent of 2x^3-x^2+1 ?

The tangent of 2x^3-x^2+1 is y=(6a_{0}^2-2a_{0})x-4a_{0}^3+a_{0}^2+1

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tangent of 2x^3-x^2+1

tangent of

2 x^{3} - x^{2} + 1

y = (6 a_{0}^{2} - 2 a_{0}) x - 4 a_{0}^{3} + a_{0}^{2} + 1

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} + 1)

Find the slope of

y = 2 x^{3} - x^{2} + 1 : \frac{d y}{d x} = 6 x^{2} - 2 x

Compute the slope of

y = 2 x^{3} - x^{2} + 1

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} + 1) : y = (6 a_{0}^{2} - 2 a_{0}) x - 4 a_{0}^{3} + a_{0}^{2} + 1

y = (6 a_{0}^{2} - 2 a_{0}) x - 4 a_{0}^{3} + a_{0}^{2} + 1

y^{^{''}} - 16 y^{^{'}} + 289 y = 4 t - 21 cos (17 t)

n = 1 \sum \infty n 2^{n}

\int \frac{1}{e ^{- x}} d x

\int \frac{2}{5} - \frac{5}{x} d x

\int \frac{1}{( 11 - 10 x - x ^{2} ) ^{2}} d x

What is the tangent of 2x^3-x^2+1 ?
The tangent of 2x^3-x^2+1 is y=(6a_{0}^2-2a_{0})x-4a_{0}^3+a_{0}^2+1