What is the tangent of f(x)= 1/(2sqrt(x)),\at x=1 ?

The tangent of f(x)= 1/(2sqrt(x)),\at x=1 is y=-1/4 x+3/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of f(x)= 1/(2sqrt(x)),\at x=1

tangent of

f (x) = \frac{1}{2 x}, at x = 1

y = - \frac{1}{4} x + \frac{3}{4}

Solution steps

Find the tangent point:

(1, \frac{1}{2})

Find the slope of

f (x) = \frac{1}{2 x} : \frac{df ( x )}{d x} = - \frac{1}{4 x ^{\frac{3}{2}}}

Compute the slope of

f (x) = \frac{1}{2 x}

x = 1 : m = - \frac{1}{4}

Find the line with slope m=

- \frac{1}{4}

and passing through

(1, \frac{1}{2}) : y = - \frac{1}{4} x + \frac{3}{4}

y = - \frac{1}{4} x + \frac{3}{4}

2 y^{^{''}} + 11 y^{^{'}} - 6 y = 0

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

f (x) = ln (1 + sin (\frac{4}{x ^{2}}))

y = sin (4 x) + sin^{2} (4 x), (0, 0)

3 y d x + 2 x d y = 0

What is the tangent of f(x)= 1/(2sqrt(x)),\at x=1 ?
The tangent of f(x)= 1/(2sqrt(x)),\at x=1 is y=-1/4 x+3/4