Question

What is the instantaneous rate of change of `f(x)=ln(2x^2-x+6)` at `x=-2`?

Answer 1

`f'(-2)=-9/16`

Explanation:

`f(x)=ln(2x^2-x+6)`

To find the instantaneous rate of change, first find `f'(x)`, then plug in `x=-2` to get `f'(-2)`

`color(red)(d/(du)(lnu)=frac{u'}{u})`

`f'(x)=frac{4x-1}{2x^2-x+6}`

`f'(-2)=frac{4(-2)-1}{2(-2)^2-(-2)+6}`

`=frac{-9}{16}`