What is the tangent of 3x^2-9 ?

The tangent of 3x^2-9 is y=6a_{0}x-3a_{0}^2-9

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tangent of 3x^2-9

tangent of

3 x^{2} - 9

y = 6 a_{0} x - 3 a_{0}^{2} - 9

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0}^{2} - 9)

Find the slope of

y = 3 x^{2} - 9 : \frac{d y}{d x} = 6 x

Compute the slope of

y = 3 x^{2} - 9

x = a_{0} : m = 6 a_{0}

Find the line with slope m=

6 a_{0}

and passing through

(a_{0}, 3 a_{0}^{2} - 9) : y = 6 a_{0} x - 3 a_{0}^{2} - 9

y = 6 a_{0} x - 3 a_{0}^{2} - 9

y^{^{'}} = \frac{e ^{x}}{y ^{2}}

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