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

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

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

tangent of

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

y = \frac{4}{3} x + \frac{4}{3}

Solution steps

Find the tangent point:

(2, 4)

Find the slope of

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

Find the line with slope m=

\frac{4}{3}

and passing through

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

y = \frac{4}{3} x + \frac{4}{3}

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