Topics for Final Exam

121.04 @ 8 AM on Friday, May 2
121.05 @ 8 AM on Thursday, May 1

• formulas that will be supplied on exam (PDF file)

Recent Topics:

• Exponential functions
  • evaluation, arithmetic rules
  • graph properties
  • base e
  • compound interest applications
• Derivatives of exponential functions
• Logarithmic functions
  • algebraic properties
  • conversion formulas
• Derivatives of logarithmic functions
• Growth and Decay applications
• Integrals, antiderivatives
  • constant of integration
  • power rule
  • method of substitution (generalized power rule)
  • finding unique solution
  • exponential rule
  • logarithmic rule
• Area, Fundamental Theorem of Calculus
  • definite integral
  • average value of a function
  • amount of an annuity

Previous Topics:

• Domains of expressions
• Sketch graphs of equations
  • intercepts, intersections
• Applications
  • revenue, cost, break-even, percent change, equilibrium (supply/demand)
• lines
  • slope, formulas, graphs
• functions
  • uniqueness, vertical line test, domain, evaluation, piecewise, composition
• limits
  • from graph, data, or formula; one-sided; non-existent
• continuity
  • from graph, data, or formula; removable
• derivative
  • definition, tangent line, slope
• Non-differentiable situations (corner, cusp, discontinuity)
• Short Cuts
  • power rule
  • constant rule
  • summation rule
  • product rule
  • quotient rule
  • chain rule
• Applications
  • slope of tangent line
  • Rates of change, average and instantaneous
  • Marginal Cost, Profit, Revenue
  • units
• Higher order derivatives
• Extrema
  • local vs absolute
  • Increasing/decreasing behavior (First Derivative Test)
  • Critical points
  • Extreme Value Theorem
  • Second Derivative Test
• Optimization