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

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

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tangent of x^2-2x+3

tangent of

x^{2} - 2 x + 3

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

Find the slope of

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

Compute the slope of

y = x^{2} - 2 x + 3

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

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

\frac{\partial}{\partial u} (v)

y = 7 x - x^{2}

f (x) = \frac{1}{1 + x ^{2}}, at x = 1

\int \frac{x ^{2}}{1 + x ^{3}} d x

\int 1 + 9 x^{2} d x

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