What is the tangent of f(x)=-2x^{2/3}-4,\at x=8 ?

The tangent of f(x)=-2x^{2/3}-4,\at x=8 is y=-2/3 x-20/3

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tangent of f(x)=-2x^{2/3}-4,\at x=8

tangent of

f (x) = - 2 x^{\frac{2}{3}} - 4, at x = 8

y = - \frac{2}{3} x - \frac{20}{3}

Solution steps

Find the tangent point:

(8, - 12)

Find the slope of

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

Compute the slope of

f (x) = - 2 x^{\frac{2}{3}} - 4

x = 8 : m = - \frac{2}{3}

Find the line with slope m=

- \frac{2}{3}

and passing through

(8, - 12) : y = - \frac{2}{3} x - \frac{20}{3}

y = - \frac{2}{3} x - \frac{20}{3}

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What is the tangent of f(x)=-2x^{2/3}-4,\at x=8 ?
The tangent of f(x)=-2x^{2/3}-4,\at x=8 is y=-2/3 x-20/3