What is the tangent of x^2+x+4 ?

The tangent of x^2+x+4 is y=(2a_{0}+1)x-a_{0}^2+4

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tangent of x^2+x+4

tangent of

x^{2} + x + 4

y = (2 a_{0} + 1) x - a_{0}^{2} + 4

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} + a_{0} + 4)

Find the slope of

y = x^{2} + x + 4 : \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} + 4) : y = (2 a_{0} + 1) x - a_{0}^{2} + 4

y = (2 a_{0} + 1) x - a_{0}^{2} + 4

What is the tangent of x^2+x+4 ?
The tangent of x^2+x+4 is y=(2a_{0}+1)x-a_{0}^2+4