What is the tangent of 2-x^2 ?

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

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tangent of 2-x^2

tangent of

2 - x^{2}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = 2 - x^{2}

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

Find the line with slope m=

- 2 a_{0}

and passing through

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

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

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