What is the tangent of f(x)=(5x+2)^{1/3},\at x=2 ?

The tangent of f(x)=(5x+2)^{1/3},\at x=2 is y= 5/(3*12^{2/3)}x+12^{1/3}-5/(3*2^{1/3)*3^{2/3}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of f(x)=(5x+2)^{1/3},\at x=2

tangent of

f (x) = (5 x + 2)^{\frac{1}{3}}, at x = 2

y = \frac{5}{3 \cdot 1 2 ^{\frac{2}{3}}} x + 1 2^{\frac{1}{3}} - \frac{5}{3 \cdot 2 ^{\frac{1}{3}} \cdot 3 ^{\frac{2}{3}}}

Solution steps

Find the tangent point:

(2, 1 2^{\frac{1}{3}})

Find the slope of

f (x) = (5 x + 2)^{\frac{1}{3}} : \frac{df ( x )}{d x} = \frac{5}{3 ( 5 x + 2 ) ^{\frac{2}{3}}}

Compute the slope of

f (x) = (5 x + 2)^{\frac{1}{3}}

x = 2 : m = \frac{5}{3 \cdot 1 2 ^{\frac{2}{3}}}

Find the line with slope m=

\frac{5}{3 \cdot 1 2 ^{\frac{2}{3}}}

and passing through

(2, 1 2^{\frac{1}{3}}) : y = \frac{5}{3 \cdot 1 2 ^{\frac{2}{3}}} x + 1 2^{\frac{1}{3}} - \frac{5}{3 \cdot 2 ^{\frac{1}{3}} \cdot 3 ^{\frac{2}{3}}}

y = \frac{5}{3 \cdot 1 2 ^{\frac{2}{3}}} x + 1 2^{\frac{1}{3}} - \frac{5}{3 \cdot 2 ^{\frac{1}{3}} \cdot 3 ^{\frac{2}{3}}}

\int_{0}^{1} (x^{2} + 4) e^{- x} d x

t \cdot e^{t}

\int_{0}^{\frac{π}{2}} cos^{2} (x) d x

cos (f (x) - 2)

\frac{1}{t ^{3}}

What is the tangent of f(x)=(5x+2)^{1/3},\at x=2 ?
The tangent of f(x)=(5x+2)^{1/3},\at x=2 is y= 5/(3*12^{2/3)}x+12^{1/3}-5/(3*2^{1/3)*3^{2/3}}