Test 3 covers the following objectives:

Section 3.7

  1. Compute the derivative of an inverse function.
  2. Evaluate derivatives involving the inverse trigonometric functions.

Section 3.9

  1. Compute the derivative of an exponential function of any base.
  2. Compute the derivative of a logarithmic function of any base.
  3. Use logarithmic differentiation.

Section 4.1

  1. Use implicit differentiation to relate rates.
  2. Solve application problems involving related rates.

Section 4.2

  1. Determine the linearization of a function at a point.
  2. Use the linearization at a point to approximate function values near the point.
  3. Compute differentials.

Section 4.3

  1. Find the critical numbers of a function.
  2. Determine whether an extreme value is absolute or relative.
  3. Find the absolute extreme values of a continuous function on a closed, bounded interval.

Section 4.5

  1. Use the first derivative to find intervals on which a function is increasing/decreasing.
  2. Use the first derivative test to locate relative extrema.
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