What is the tangent of f(x)=-9x^{1/3}+5,\at x=27 ?

The tangent of f(x)=-9x^{1/3}+5,\at x=27 is y=-1/3 x-13

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tangent of f(x)=-9x^{1/3}+5,\at x=27

tangent of

f (x) = - 9 x^{\frac{1}{3}} + 5, at x = 27

y = - \frac{1}{3} x - 13

Solution steps

Find the tangent point:

(27, - 22)

Find the slope of

f (x) = - 9 x^{\frac{1}{3}} + 5 : \frac{df ( x )}{d x} = - \frac{3}{x ^{\frac{2}{3}}}

Compute the slope of

f (x) = - 9 x^{\frac{1}{3}} + 5

x = 27 : m = - \frac{1}{3}

Find the line with slope m=

- \frac{1}{3}

and passing through

(27, - 22) : y = - \frac{1}{3} x - 13

y = - \frac{1}{3} x - 13

x \to \infty lim (\frac{7}{x} - 9)

\int 45 x^{2} ln (x) d x

\frac{d}{d x} (\frac{x}{9})

f (x) = tan (\frac{1}{x})

\frac{d}{d x} (\frac{100 x}{x + y}) = 0

What is the tangent of f(x)=-9x^{1/3}+5,\at x=27 ?
The tangent of f(x)=-9x^{1/3}+5,\at x=27 is y=-1/3 x-13