What is the tangent of x^2+2x-1 ?

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

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tangent of x^2+2x-1

tangent of

x^{2} + 2 x - 1

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} + 2 a_{0} - 1)

Find the slope of

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

Compute the slope of

y = x^{2} + 2 x - 1

x = a_{0} : m = 2 a_{0} + 2

Find the line with slope m=

2 a_{0} + 2

and passing through

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

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

\int \frac{9 ^{2 x + 5}}{3} d x

\int_{3}^{6} 1 + x^{4} + 2 x^{2} d x

\frac{d}{d x} ((x^{2} + 5 x - 6) (x^{3} + 5 x - 8))

\int (3 x - 2)^{2} d x

f (x) = 3 + e^{x}

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