What is the tangent of 2/5 x^2+1/4 x-1 ?

The tangent of 2/5 x^2+1/4 x-1 is y=((4a_{0})/5+1/4)x-(2a_{0}^2)/5-1

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tangent of 2/5 x^2+1/4 x-1

tangent of

\frac{2}{5} x^{2} + \frac{1}{4} x - 1

y = (\frac{4 a _{0}}{5} + \frac{1}{4}) x - \frac{2 a _{0}^{2}}{5} - 1

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{5} a_{0}^{2} + \frac{1}{4} a_{0} - 1)

Find the slope of

y = \frac{2}{5} x^{2} + \frac{1}{4} x - 1 : \frac{d y}{d x} = \frac{4 x}{5} + \frac{1}{4}

Compute the slope of

y = \frac{2}{5} x^{2} + \frac{1}{4} x - 1

x = a_{0} : m = \frac{4 a _{0}}{5} + \frac{1}{4}

Find the line with slope m=

\frac{4 a _{0}}{5} + \frac{1}{4}

and passing through

(a_{0}, \frac{2}{5} a_{0}^{2} + \frac{1}{4} a_{0} - 1) : y = (\frac{4 a _{0}}{5} + \frac{1}{4}) x - \frac{2 a _{0}^{2}}{5} - 1

y = (\frac{4 a _{0}}{5} + \frac{1}{4}) x - \frac{2 a _{0}^{2}}{5} - 1

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What is the tangent of 2/5 x^2+1/4 x-1 ?
The tangent of 2/5 x^2+1/4 x-1 is y=((4a_{0})/5+1/4)x-(2a_{0}^2)/5-1