Test 3 covers the following objectives:
- Compute the derivative of an inverse function.
- Evaluate derivatives involving the inverse trigonometric functions.
- Compute the derivative of an exponential function of any base.
- Compute the derivative of a logarithmic function of any base.
- Use logarithmic differentiation.
- Use implicit differentiation to relate rates.
- Solve application problems involving related rates.
- Determine the linearization of a function at a point.
- Use the linearization at a point to approximate function values near the point.
- Compute differentials.
- Find the critical numbers of a function.
- Determine whether an extreme value is absolute or relative.
- Find the absolute extreme values of a continuous function on a closed, bounded interval.
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- Use the first derivative to find intervals on which a function is increasing/decreasing.
- Use the first derivative test to locate relative extrema.