What is the tangent of x^2+x+3 ?

The tangent of x^2+x+3 is y=(2a_{0}+1)x-a_{0}^2+3

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tangent of x^2+x+3

tangent of

x^{2} + x + 3

y = (2 a_{0} + 1) x - a_{0}^{2} + 3

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} + a_{0} + 3)

Find the slope of

y = x^{2} + x + 3 : \frac{d y}{d x} = 2 x + 1

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 = 2 a_{0} + 1

Find the line with slope m=

2 a_{0} + 1

and passing through

(a_{0}, a_{0}^{2} + a_{0} + 3) : y = (2 a_{0} + 1) x - a_{0}^{2} + 3

y = (2 a_{0} + 1) x - a_{0}^{2} + 3

\int \frac{1}{2 y ^{2}} d y

\int_{0}^{3} (x^{2} + 1) d x

n = 0 \sum \infty \frac{3}{n}

\int (x + 2)^{- \frac{1}{2}} d x

\int (8 x) d x

What is the tangent of x^2+x+3 ?
The tangent of x^2+x+3 is y=(2a_{0}+1)x-a_{0}^2+3