For the last 25 minutes, we went over the study guide. The answers for 16 - 22 are below.
NOTE: 22d should say x = 2 and 22f should say x = 1.
16. dA/dt = 20 pi cm^2/min
17. dV/dt = 588 pi cubic inches/minute
18. dV/dt = 288 cubic cm/second
19. dh/dt = 2/(5 pi) or 0.127 feet/minute
20. dy/dt = -0.6755 feet/second
21. v(t) = -9.8t + 140 v(4) = 100.8 m/s
22 c) right since v(3)> 0
22 d) slowing down since v(2) >0 and a (2) < 0
22e) at t = o the particle is at rest since v(0) = 0
22 f) right since v(1) > 0
Test is tomorrow. Students are able to 1) Use the constant, power, product & quotient rules and CHAIN Rule to find the derivative (trig included)
2) Be able to write the equation of a tangent line (know that the derivative is the slope of the tangent line)
3) Find a derivative given a graph or a data table
4) Know how to find a derivative using implicit differentiation
5) Be able to identify x or y values where there is a horizontal or vertical tangent line
6) Be able to find the velocity or acceleration of a particle given its position equation; determine which way a particle is traveling, determine when it is at rest, determine if it is speeding up or slowing down, determine if the velocity is increasing or decreasing at a specific moment in time. Students will provided proper justifications for their answers.
7) Be able to set up and solve related rates problems.