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

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

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tangent of 3x-2x^2

tangent of

3 x - 2 x^{2}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = 3 x - 2 x^{2}

x = a_{0} : m = 3 - 4 a_{0}

Find the line with slope m=

3 - 4 a_{0}

and passing through

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

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

x \to 0 lim ((e^{- \frac{1}{x}})^{x})

\frac{d y}{d t} + t y = t y^{2}

\int x e^{2 x y} d y

\int x \cdot \frac{1}{x} d x

\int x^{3} + e^{x} + 2 d x

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