What is the tangent of 2x^2+10x+9 ?

The tangent of 2x^2+10x+9 is y=(4a_{0}+10)x-2a_{0}^2+9

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tangent of 2x^2+10x+9

tangent of

2 x^{2} + 10 x + 9

y = (4 a_{0} + 10) x - 2 a_{0}^{2} + 9

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{2} + 10 a_{0} + 9)

Find the slope of

y = 2 x^{2} + 10 x + 9 : \frac{d y}{d x} = 4 x + 10

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} + 10

Find the line with slope m=

4 a_{0} + 10

and passing through

(a_{0}, 2 a_{0}^{2} + 10 a_{0} + 9) : y = (4 a_{0} + 10) x - 2 a_{0}^{2} + 9

y = (4 a_{0} + 10) x - 2 a_{0}^{2} + 9

What is the tangent of 2x^2+10x+9 ?
The tangent of 2x^2+10x+9 is y=(4a_{0}+10)x-2a_{0}^2+9