Rates of Change with equations and limits

• Type of Rate of Change

  • Average
  • Instantaneous
• Graphically

  • (a,f(a)) and (b,f(b))
  • (a,f(a))
• Algebraically

  • f(b) - f(a) / b - a
  • Limit as h->0 of (f(a+h) - f(a)) / h
• Difference quotient

  The algebraic expression used to find the slope of the secant between P(a,f(a)) and Q(a+h,f(a+h))
• How can we use the difference quotient to help us estimate the slope of the tangent at x=a?

  Take the limit as h->0 of the difference quotient