What is the tangent of 3x-5x^2 ?

The tangent of 3x-5x^2 is y=(3-10a_{0})x+5a_{0}^2

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tangent of 3x-5x^2

tangent of

3 x - 5 x^{2}

y = (3 - 10 a_{0}) x + 5 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} - 5 a_{0}^{2})

Find the slope of

y = 3 x - 5 x^{2} : \frac{d y}{d x} = 3 - 10 x

Compute the slope of

y = 3 x - 5 x^{2}

x = a_{0} : m = 3 - 10 a_{0}

Find the line with slope m=

3 - 10 a_{0}

and passing through

(a_{0}, 3 a_{0} - 5 a_{0}^{2}) : y = (3 - 10 a_{0}) x + 5 a_{0}^{2}

y = (3 - 10 a_{0}) x + 5 a_{0}^{2}

\frac{\partial}{\partial x} (e^{∣ x yz ∣})

\frac{\partial}{\partial y} (y^{2} - 2 x y + 6 x)

\int_{0}^{1} \frac{x}{e ^{x^{2}}} d x

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

\int \frac{1}{cos ( 8 x )} d x

What is the tangent of 3x-5x^2 ?
The tangent of 3x-5x^2 is y=(3-10a_{0})x+5a_{0}^2