Related Rates

Question 1

Basic Rate Problem

• Draw picture
• Write _
• Write formula
• Take derivative
  
  • Remember chain rule
  • Remember product rule
  • Remember quotient rule
  • Each variable in the formula will have a _ (even )
  • Rates = 0 if not _
  • Make sure a rate is _ if it is getting smaller
• Replace with knowns
• Solve
• Units
  
  • Length = units
  • Area = units2
  • Volume = units3
• Three significant figures

Answer 1

Knowns, derivative, changing, negative

Question 2

Shadow Problem

• Draw picture
• Write down known
• Make ratios with _ values
• Cross multiply
• Take _
  
  • “Shadow lengthening” = dy/dt
  • “Tip of shadow lengthening” = dz/dt
• Solve
  
  • X1 + X2 = Z
  • dX1/dt + dX2/dt = dZ/dt
• Units
• Three significant figures

Answer 2

Proportional, derivative

Question 3

Cone and Cylinder

• Draw a picture
• Write knowns
• Make a ratio with _ and _ in terms of r
• Write formula
• Take _
• Solve
• Units
• Three significant figures

Answer 3

h, r, derivative