Question

What is the instantaneous rate of change of `f(x)=sqrt(3x^2-4x+5)` at `x=-1`?

Answer 1

It is `f'(-1)=-5/[2sqrt3]`

Explanation:

The rate of change is the value of the first derivative of the function `f(x)` at `x=-1`

Hence

`f'(x)=[3x-2]/sqrt[3x^2-4x+5]`

so

`f'(-1)=-5/[2sqrt3]`