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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of y=7x-x^2

tangent of

y = 7 x - x^{2}

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

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} = 7 - 2 x

Compute the slope of

y = 7 x - x^{2}

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

Find the line with slope m=

7 - 2 a_{0}

and passing through

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

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

\int_{- 1}^{1} \frac{10}{x ^{2}} d x

\int_{3}^{12} (6 x + 1) d x

\int (\frac{1}{x ^{10}} - x^{10} - \frac{1}{3}) d x

4 t^{3} cos (t)

\int_{- \infty}^{12} r e^{\frac{r}{3}} d r

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