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

The tangent of (4x+4)^{1/3},\at x=2 is y= 4/(3*12^{2/3)}x+12^{1/3}-(2*2^{2/3})/(3*3^{2/3)}

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tangent of (4x+4)^{1/3},\at x=2

tangent of

(4 x + 4)^{\frac{1}{3}}, at x = 2

y = \frac{4}{3 \cdot 1 2 ^{\frac{2}{3}}} x + 1 2^{\frac{1}{3}} - \frac{2 \cdot 2 ^{\frac{2}{3}}}{3 \cdot 3 ^{\frac{2}{3}}}

Solution steps

Find the tangent point:

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

Find the slope of

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

Find the line with slope m=

\frac{4}{3 \cdot 1 2 ^{\frac{2}{3}}}

and passing through

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

y = \frac{4}{3 \cdot 1 2 ^{\frac{2}{3}}} x + 1 2^{\frac{1}{3}} - \frac{2 \cdot 2 ^{\frac{2}{3}}}{3 \cdot 3 ^{\frac{2}{3}}}

What is the tangent of (4x+4)^{1/3},\at x=2 ?
The tangent of (4x+4)^{1/3},\at x=2 is y= 4/(3*12^{2/3)}x+12^{1/3}-(2*2^{2/3})/(3*3^{2/3)}