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

Compute the slope of

y = x^{2} + x + 4

x = a_{0} : 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

y^{^{''}} - 3 y^{^{'}} + 7 y = 4 e^{3 t}

\frac{d}{d x} (\frac{8.7 x + 0.2}{x ^{2} - 4.5 x + 7.5})

x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

f (x) = x^{3} - 3 x - 5, at x = 1

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