What is the tangent of 9+5x^2 ?

The tangent of 9+5x^2 is y=10a_{0}x+9-5a_{0}^2

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tangent of 9+5x^2

tangent of

9 + 5 x^{2}

y = 10 a_{0} x + 9 - 5 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 9 + 5 a_{0}^{2})

Find the slope of

y = 9 + 5 x^{2} : \frac{d y}{d x} = 10 x

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 10 a_{0}

Find the line with slope m=

10 a_{0}

and passing through

(a_{0}, 9 + 5 a_{0}^{2}) : y = 10 a_{0} x + 9 - 5 a_{0}^{2}

y = 10 a_{0} x + 9 - 5 a_{0}^{2}