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

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

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tangent of 5x^2+5x+2

tangent of

5 x^{2} + 5 x + 2

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

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} + 5

Find the line with slope m=

10 a_{0} + 5

and passing through

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

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

What is the tangent of 5x^2+5x+2 ?
The tangent of 5x^2+5x+2 is y=(10a_{0}+5)x-5a_{0}^2+2