Calc Iroc and difference quotient question

Question

 If the height of a sea gull is shown to follow the function h(t)=3sin(pi/8 t)+15 where t is in seconds and h is in meters estimate the instantaneous rate of change at t=3 using the difference quotient with an h of 0.01

Answer 1

An approximation of i.r.o.c. using the difference quotient is just a fancy way of asking you to use the slope formula you've known since 7th grade: m = (y₂ - y₁)/(x₂ - x₁) .

If you want to approximate i.r.o.c. at t = 3 with an h = .01 you could use (3 , h(3)) and (3.01 , h(3.01)) as the two points. Or, for a better approximation, "straddle" t = 3 by using (2.995 , h(2.995)) and (3.005 , h(3.005)).