What is the tangent of f(x)=1\sqrt[3]{x},\at x=1 ?

The tangent of f(x)=1\sqrt[3]{x},\at x=1 is y= 1/3 x+2/3

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tangent of f(x)=1\sqrt[3]{x},\at x=1

tangent of

f (x) = 1 3 x, at x = 1

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

Solution steps

Find the tangent point:

(1, 1)

Find the slope of

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{1}{3}

Find the line with slope m=

\frac{1}{3}

and passing through

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

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

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What is the tangent of f(x)=1\sqrt[3]{x},\at x=1 ?
The tangent of f(x)=1\sqrt[3]{x},\at x=1 is y= 1/3 x+2/3