Question

1) find the slope of the line tangent to f(x)=6/sq(x) at point (9,2)

Answer 1

$f(x)=\frac{6}{\sqrt[]{x}}$

First, we need to find the first derivate

$\begin{gathered} f^{}(x)=6x^{-\frac{1}{2}} \\ f^{\prime}(x)=-\frac{1}{2}6x^{-\frac{1}{2}-1}=-3x^{-\frac{3}{2}}=-\frac{3}{\sqrt[]{x^3}} \end{gathered}$

Plug x value of the indicated point into f '(x) to find the slope at x.

$f^{\prime}(9)=-\frac{3}{\sqrt[]{9^3}}$$f^{\prime}(9)=-\frac{1}{9}$

the slope of the line is -1/9

the slope of the tangent line is the inverse of -1/9

the slope of the tangent line is 9