What is the tangent of 6-4x^2 ?

The tangent of 6-4x^2 is y=-8a_{0}x+6+4a_{0}^2

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tangent of 6-4x^2

tangent of

6 - 4 x^{2}

y = - 8 a_{0} x + 6 + 4 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 6 - 4 a_{0}^{2})

Find the slope of

y = 6 - 4 x^{2} : \frac{d y}{d x} = - 8 x

Compute the slope of

y = 6 - 4 x^{2}

x = a_{0} : m = - 8 a_{0}

Find the line with slope m=

- 8 a_{0}

and passing through

(a_{0}, 6 - 4 a_{0}^{2}) : y = - 8 a_{0} x + 6 + 4 a_{0}^{2}

y = - 8 a_{0} x + 6 + 4 a_{0}^{2}

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