Question

I need to know instantaneous rate of change at t=2

Answer 1

`g(t)=4-t^2`


`\displaystyle g'(2)=\lim_(t\to2)(g(t)-g(2))/(t-2)`

`\displaystyle g'(2)=\lim_(t\to2)(4-t^2-0)/(t-2)`

`\displaystyle g'(2)=-\lim_(t\to2)((2-t)(2+t))/(2-t)`

`\displaystyle g'(2)=-\lim_(t\to2)(2+t)`

`\displaystyle g'(2)=-4`