What is the tangent of x^2+x ?

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

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tangent of x^2+x

tangent of

x^{2} + x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = x^{2} + x

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

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

(x + 1)^{3} (x - 1)

6 y^{^{''}} - 11 y^{^{'}} + 3 y = 0

(- 1, 1), (4, - 2)

\int_{- 1}^{5} (x - 2)^{2} d x

x \to 6 lim (\frac{x ^{2} - 1}{x - 6})