What is the tangent of-x^2+3x+7 ?

The tangent of-x^2+3x+7 is y=(-2a_{0}+3)x+a_{0}^2+7

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tangent of-x^2+3x+7

tangent of

- x^{2} + 3 x + 7

y = (- 2 a_{0} + 3) x + a_{0}^{2} + 7

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - a_{0}^{2} + 3 a_{0} + 7)

Find the slope of

y = - x^{2} + 3 x + 7 : \frac{d y}{d x} = - 2 x + 3

Compute the slope of

y = - x^{2} + 3 x + 7

x = a_{0} : m = - 2 a_{0} + 3

Find the line with slope m=

- 2 a_{0} + 3

and passing through

(a_{0}, - a_{0}^{2} + 3 a_{0} + 7) : y = (- 2 a_{0} + 3) x + a_{0}^{2} + 7

y = (- 2 a_{0} + 3) x + a_{0}^{2} + 7

\frac{d}{d y} (\frac{y}{z})

\int \frac{1}{x ^{2} + 4 x + 68} d x

\frac{\partial}{\partial x} (arctan (\frac{x}{y}))

\frac{d}{d x} (4 x^{3} - 12 x)

\int_{3}^{5} \frac{2 x ^{2} + x + 4}{x - 1} d x

What is the tangent of-x^2+3x+7 ?
The tangent of-x^2+3x+7 is y=(-2a_{0}+3)x+a_{0}^2+7