An object moving along a straight line path has a differentiable position function y=s(t). It is known that at time t=9 seconds, the object's position is s=4 feet (measured from its starting point at t=0). Furthermore, the object's instantaneous velocity at t=9 is -1.2 feet per second, and its acceleration at the same instant is 0.08 feet per second.
1) Use local linearity to estimate the position of the object at t=9.34
2) Is your estimate likely too large or too small? why?

Question

An object moving along a straight line path has a differentiable position function y=s(t). It is known that at time t=9 seconds, the object's position is s=4 feet (measured from its starting point at t=0). Furthermore, the object's instantaneous velocity at t=9 is -1.2 feet per second, and its acceleration at the same instant is 0.08 feet per second.
1) Use local linearity to estimate the position of the object at t=9.34
2) Is your estimate likely too large or too small? why?