Question

If `f(x)=4x^(-1)` find `(f(a+h)-f(a))/h`?

Answer 1

`(f(a+h)-f(a))/h=(-4)/(a(a+h))`

Explanation:

As `f(x)=4x^(-1)=4/x`

as such `f(a)=4/a` and `f(a+h)=4/(a+h)`

and `(f(a+h)-f(a))/h=(4/(a+h)-4/a)/h`

= `((4a-4a-4h)/(a(a+h)))/h`

= `((-4h)/(a(a+h)))/h`

= `(-4h)/(a(a+h))xx1/h`

= `(-4)/(a(a+h))`