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^{-(1)/(2)} \\ f^(\prime)(x)=-(1)/(2)6x^{-(1)/(2)-1}=-3x^{-(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)=-(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