Applications of Derivatives · Applied Problems
Differentials
The differential dy approximates the change in y for a small change dx. Used for error estimation and approximation.
Worked examples
Use differentials to approximate the change in y = x³ when x changes from 2 to 2.01.
- dy = f'(x) dx = 3x² dx
- dy = 3(4)(0.01) = 0.12
Answer: dy = 0.12 (actual Δy = 0.120601)
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