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

The tangent of 7-x-x^2 is y=(-2a_{0}-1)x+a_{0}^2+7

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tangent of 7-x-x^2

tangent of

7 - x - x^{2}

y = (- 2 a_{0} - 1) x + a_{0}^{2} + 7

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = 7 - x - x^{2} : \frac{d y}{d x} = - 2 x - 1

Compute the slope of

y = 7 - x - x^{2}

x = a_{0} : m = - 2 a_{0} - 1

Find the line with slope m=

- 2 a_{0} - 1

and passing through

(a_{0}, 7 - a_{0} - a_{0}^{2}) : y = (- 2 a_{0} - 1) x + a_{0}^{2} + 7

y = (- 2 a_{0} - 1) x + a_{0}^{2} + 7

x \to 3 - lim (\frac{x}{x ^{2} - 9})

\frac{\partial}{\partial x} (β (x)^{- γ})

\int_{l n (3)}^{l n (7)} e^{x} d x

\frac{\partial}{\partial y} (x + e^{4 y})

\frac{d}{d x} ((2 - x) (y - 2) (3 - x - y))

What is the tangent of 7-x-x^2 ?
The tangent of 7-x-x^2 is y=(-2a_{0}-1)x+a_{0}^2+7