What is the tangent of x^2-7x+12 ?

The tangent of x^2-7x+12 is y=(2a_{0}-7)x-a_{0}^2+12

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tangent of x^2-7x+12

tangent of

x^{2} - 7 x + 12

y = (2 a_{0} - 7) x - a_{0}^{2} + 12

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} - 7 a_{0} + 12)

Find the slope of

y = x^{2} - 7 x + 12 : \frac{d y}{d x} = 2 x - 7

Compute the slope of

y = x^{2} - 7 x + 12

x = a_{0} : m = 2 a_{0} - 7

Find the line with slope m=

2 a_{0} - 7

and passing through

(a_{0}, a_{0}^{2} - 7 a_{0} + 12) : y = (2 a_{0} - 7) x - a_{0}^{2} + 12

y = (2 a_{0} - 7) x - a_{0}^{2} + 12

\int \frac{2 x ^{2} - x - 20}{x ^{2} + x - 6} d x

\int 8 x sec (x) tan (x) d x

\frac{\partial}{\partial x} (x y (- 3 - x - y))

\int \frac{y}{2} d y

(4 x^{2} - 13)^{- 13}

What is the tangent of x^2-7x+12 ?
The tangent of x^2-7x+12 is y=(2a_{0}-7)x-a_{0}^2+12