Calculus Final Review Test 1 (Unit 16-17)

• Related rates

  Every variable depends on time and has to use implicit differentiation on EVERY variable not just y
• Volume of a sphere

  V = 4/3πr^3
• d/dt(x)

  dx/dt
• d/dt(y)

  dy/dt
• d/dt(x^2 y)

  2x dx/dt (y) + x^2 (dy/dt)
• Area of a circle

  πr^2
• Volume of a cylinder

  V = πr^2h
• Volume of a cone

  V=1/3πr^2h
• Solving a related rates problem

  Decide what the two variables are

  Find an equation relating them

  Take d/dt of both sides

  Plug the "when" information into the equation

  Solve for the unknown rate