What is the tangent of 5x-x^2 ?

The tangent of 5x-x^2 is y=(5-2a_{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 5x-x^2

tangent of

5 x - x^{2}

y = (5 - 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}, 5 a_{0} - a_{0}^{2})

Find the slope of

y = 5 x - x^{2} : \frac{d y}{d x} = 5 - 2 x

Compute the slope of

y = 5 x - x^{2}

x = a_{0} : m = 5 - 2 a_{0}

Find the line with slope m=

5 - 2 a_{0}

and passing through

(a_{0}, 5 a_{0} - a_{0}^{2}) : y = (5 - 2 a_{0}) x + a_{0}^{2}

y = (5 - 2 a_{0}) x + a_{0}^{2}

\int_{0}^{1} 23 (\frac{e ^{\frac{1}{x}}}{x ^{3}}) d x

x \to - 4 lim (\frac{1}{x + 4})

\int \frac{x + 1}{x + 10} d x

f (x) = x^{2}, (0, 3)

\int \frac{1}{e ^{x} e ^{2 x} - 9} d x