What is the tangent of y=7x^2+2x+1 ?

The tangent of y=7x^2+2x+1 is y=(14a_{0}+2)x-7a_{0}^2+1

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tangent of y=7x^2+2x+1

tangent of

y = 7 x^{2} + 2 x + 1

y = (14 a_{0} + 2) x - 7 a_{0}^{2} + 1

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 7 a_{0}^{2} + 2 a_{0} + 1)

Find the slope of

y = 7 x^{2} + 2 x + 1 : \frac{d y}{d x} = 14 x + 2

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 = 14 a_{0} + 2

Find the line with slope m=

14 a_{0} + 2

and passing through

(a_{0}, 7 a_{0}^{2} + 2 a_{0} + 1) : y = (14 a_{0} + 2) x - 7 a_{0}^{2} + 1

y = (14 a_{0} + 2) x - 7 a_{0}^{2} + 1

What is the tangent of y=7x^2+2x+1 ?
The tangent of y=7x^2+2x+1 is y=(14a_{0}+2)x-7a_{0}^2+1