Calculus I

  1. Functions: I can
    • evaluate limits using the Limit Laws,
    • determine whether a function is continuous,
    • use the Intermediate Value Theorem to solve problems.
  2. Derivatives: I can
    • compute the derivative from the Limit Definition,
    • find the line tangent to a function at a point,
    • find the instantaneous rate of change of a function at a point,
    • find the average rate of change of a function on an interval.
  3. Derivative Rules: I can
    • use the power rule to find the derivative of a monomial,
    • use the sum/difference rule to find the derivative of a sum/difference of functions,
    • use the constant multiple rule to find the derivative a constant multiple of a function.
  4. Product and Quotient Rules: I can
    • use the product rule to find the derivative of a product of functions,
    • use the quotient rule to find the derivative of a rational function.
  5. Implicit Differentiation and Related Rates: I can
    • use the method of Implicit Differentiation to solve Related Rates problems.
  6. Chain Rule: I can
    • use the Chain Rule to find the derivative of a composition of functions.
  7. Derivatives and Shape: I can
    • find critical numbers of a function,
    • perform the First Derivative Test,
    • perform the Increasing/Decreasing Test,
    • perform the Second Derivative Test,
    • determine the concavity of a function and find its inflection points.
  8. Asymptotes: I can
    • determine the horizontal asymptotes of a function,
    • determine the vertical asymptotes of a function,
    • determine the slant/oblique asymptotes of a function.
  9. Curve Sketching: I can
    • use the skills from the Derivatives and Shape and Asymptotes standards to sketch a graph of a function.
  10. Closed Interval Method and Optimization: I can
    • find the maximum of a function on a closed interval,
    • find the minimum of a function on a closed interval.
  11. Integrals: I can
    • approximate the area under a curve using Riemann sums,
    • evaluate definite integrals using the limit definition.
  12. Fundamental Theorem of Calculus: I can
    • find the anti-derivative of a given function and evaluate indefinite integrals,
    • use the anti-derivative to evaluate a definite integral.
  13. Substitution: I can
    • use substitution to evaluate indefinite integrals,
    • use substitution to evaluate definite integrals.
  14. Inverse Functions: I can
    • use the properties of the exponential to solve problems,
    • use the properties of the logarithm to solve problems.
  15. Calculus of Inverse Functions: I can
    • evaluate derivatives and integrals involving exponentials,
    • evaluate derivatives and integrals involving logarithms.