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

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

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

tangent of

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

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

Find the slope of

y = 2 x^{3} - 2 x^{2} + 1 : \frac{d y}{d x} = 6 x^{2} - 4 x

Compute the slope of

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

x = a_{0} : m = 6 a_{0}^{2} - 4 a_{0}

Find the line with slope m=

6 a_{0}^{2} - 4 a_{0}

and passing through

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

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

\frac{d}{d x} (n \cdot ln (x))

\frac{d}{d x} (\frac{3 x ^{2} - 1}{6 x ^{3} + 5})

x \to 7 + lim (\frac{3}{x - 7})

\int_{5}^{\infty} \frac{1}{x ^{2} - 4} d x

\frac{d}{d x} (\frac{1}{4 x ^{2} + 2 x})

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