What is the tangent of 2x^2-5 ?

The tangent of 2x^2-5 is y=4a_{0}x-2a_{0}^2-5

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tangent of 2x^2-5

tangent of

2 x^{2} - 5

y = 4 a_{0} x - 2 a_{0}^{2} - 5

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{2} - 5)

Find the slope of

y = 2 x^{2} - 5 : \frac{d y}{d x} = 4 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 = 4 a_{0}

Find the line with slope m=

4 a_{0}

and passing through

(a_{0}, 2 a_{0}^{2} - 5) : y = 4 a_{0} x - 2 a_{0}^{2} - 5

y = 4 a_{0} x - 2 a_{0}^{2} - 5