What is the tangent of 6-x^2 ?

The tangent of 6-x^2 is y=-2a_{0}x+6+a_{0}^2

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tangent of 6-x^2

tangent of

6 - x^{2}

y = - 2 a_{0} x + 6 + a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 6 - a_{0}^{2})

Find the slope of

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

Compute the slope of

y = 6 - x^{2}

x = a_{0} : m = - 2 a_{0}

Find the line with slope m=

- 2 a_{0}

and passing through

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

y = - 2 a_{0} x + 6 + a_{0}^{2}

ln (\frac{1}{3}) (2 + e^{- 3 x})

\int e^{t + 2} d t

\frac{d}{d y} (4 9 - y)

y^{^{'}} = 3 x (x - 1)