Question

How do you find the equation of the line tangent to the graph of `f(x) =10/(5x + 9`), when x =1/5?

Answer 1

`y=-1/2x+11/10`

Explanation:

The equation of the Tangent line has the form `y=mx+n`

At first we will compute the first derivative of `f(x)`

`f(x)=10(5x+9)^(-1)`
then we get

`f'(x)=-10(5x+9)^(-2)*5=-50/(5x+9)^2` by the chain rule.
and

`f'(1/5)=-50/(5*1/5+9)^2=-50/100=-1/2`
so the slope is given by `m=-1/2`

The Point is given by `f(1/5)=10/10=1`

so we have
`1=-1/2*(1/5)+n`

so `n=11/10`