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

The tangent of f(x)=(4x+4)^{1/3},\at x=1 is y= 1/3 x+5/3

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tangent of f(x)=(4x+4)^{1/3},\at x=1

tangent of

f (x) = (4 x + 4)^{\frac{1}{3}}, at x = 1

y = \frac{1}{3} x + \frac{5}{3}

Solution steps

Find the tangent point:

(1, 2)

Find the slope of

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

Compute the slope of

f (x) = (4 x + 4)^{\frac{1}{3}}

x = 1 : m = \frac{1}{3}

Find the line with slope m=

\frac{1}{3}

and passing through

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

y = \frac{1}{3} x + \frac{5}{3}

\int 10 x - x^{2} d x

\int (x^{\frac{2}{3}} + 3) d x

y = arcsin (\frac{x}{6})

f (x) = x^{2} + 6

\int_{0}^{1} 36 π (x^{2} - x^{10}) d x

What is the tangent of f(x)=(4x+4)^{1/3},\at x=1 ?
The tangent of f(x)=(4x+4)^{1/3},\at x=1 is y= 1/3 x+5/3