1. (a) Find the slope of the tangent line to the curve \(y=x^2-x+1\) at \((4,13)\).


Solution


(b) Find an equation of the tangent line in part (a).


Solution


2. Find an equation of the tangent line to the curve \(y=\sqrt{x+2}\) at \((7,3)\).


Solution


3. The displacement (in meters) of a particle moving in a straight line is given by \( s(t)= 2t^2+3\), where \(t\) is measured in seconds.
(a) Find the average velocity over the time interval \([1,3]\).


Solution


(b) Find the instantaneous velocity at \(t=1\).


Solution