Question

How do you find the slope of a tangent line to the graph of the function `f(x) = 10/(7x)` at (1,10/7)?

Answer 1

`-10/7`.

Explanation:

The slope of a tangent line to the graph of the function `y=f(x)` at

the point `P(x_0,f(x_0))` is `[dy/dx]_(P(x_0,f(x_0)))=f'(x_0)`.

For `f(x)=10/(7x)`, we have,

`f'(x)=10/7*d/dx(1/x)=10/7*-1/x^2=-10/(7x^2)`.

`:."The Reqd. Slope="-10/(7*1^2)=-10/7`.