What is the tangent of f(x)=(4x-7)^{1/2},\at x=4 ?

The tangent of f(x)=(4x-7)^{1/2},\at x=4 is y= 2/3 x+1/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of f(x)=(4x-7)^{1/2},\at x=4

tangent of

f (x) = (4 x - 7)^{\frac{1}{2}}, at x = 4

y = \frac{2}{3} x + \frac{1}{3}

Solution steps

Find the tangent point:

(4, 3)

Find the slope of

f (x) = (4 x - 7)^{\frac{1}{2}} : \frac{df ( x )}{d x} = \frac{2}{( 4 x - 7 ) ^{\frac{1}{2}}}

Compute the slope of

f (x) = (4 x - 7)^{\frac{1}{2}}

x = 4 : m = \frac{2}{3}

Find the line with slope m=

\frac{2}{3}

and passing through

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

y = \frac{2}{3} x + \frac{1}{3}

\int e^{x} x^{2} d x

\frac{1}{e ^{y}} y^{^{'}} = \frac{1}{e ^{x}}

\int \frac{x ^{3} - 8}{x - 2} d x

\frac{5}{12} (3 + 5) a^{3}

\int x^{2} + y^{5} d y

What is the tangent of f(x)=(4x-7)^{1/2},\at x=4 ?
The tangent of f(x)=(4x-7)^{1/2},\at x=4 is y= 2/3 x+1/3