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

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Answer 1 · 2017-03-25T14:45:29

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

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

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

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

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

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

$=frac{-9}{16}$

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