Calculus
Applications of Derivatives flashcards
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- What does “Position and Velocity” mean?Motion
- The signed instantaneous rate of position change.
- What important condition applies to position and velocity?Motion
- Negative velocity describes direction, not a negative speed magnitude.
- What does “Velocity and Acceleration” mean?Motion
- The instantaneous rate of change of signed velocity.
- What important condition applies to velocity and acceleration?Motion
- Positive acceleration does not always mean increasing speed.
- What does “Related Rates for Area” mean?Related Rates
- Finding an area rate from a linked radius rate.
- What important condition applies to related rates for area?Related Rates
- Use the chain-rule factor dr/dt.
- What does “Related Rates for Volume” mean?Related Rates
- A volume-change rate determined by a sphere’s radius-change rate.
- What important condition applies to related rates for volume?Related Rates
- Differentiate before substituting the instantaneous radius.
- What does “Linear Approximation” mean?Linear Approximation
- Approximating a nearby function value using its tangent line.
- What important condition applies to linear approximation?Linear Approximation
- A tangent estimate should not be presented as an exact value without justification.
- What does “Differentials” mean?Linear Approximation
- The first-order predicted change associated with an input increment.
- What important condition applies to differentials?Linear Approximation
- dy and the actual Δy are generally different.