MATH 140 Lecture 12: Rates of Change and Related Rates

• School: PSU
• Department: Mathematics
• Course: MATH 140
• Professor: Chopra, Parsons

Document Summary

Math 140 - lecture 12 - rates of change and related rates. Rates of change in the natural and social sciences. , then the derivative dy dx is the rate of change of y with respect to. The average rate of change of y with respect to x over the interval x. The instantaneous rate of change of y with respect to x s=f (t) is the position function of a particle moving in a straight line. T represents the average velocity over time t represents the instantaneous velocity v= ds dt a(t )=v" (t)=s" "(t) Acceleration is the instantaneous rate of change of velocity with respect to time. Example: the position of a particle is given by the equation s=f (t)=t3 6t2+9t. Find velocity at time t. what is the velocity after 2 s? v= ds dt. Recall that the velocity function is the derivative of the position function v(2)=3 (2)2 12(2)+9= 3 m/s.