Derivative by Definition Worksheet
Understand and apply the definition of the derivative to calculate derivatives of various functions.
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Standards
Derivative by Definition
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Carefully read each question and use the definition of the derivative to find the solution. Show all your work.
1. State the formal definition of the derivative of a function f(x).
2. The derivative of a function at a point gives the slope of the line to the function's graph at that point.
3. The process of finding the derivative is called .
4. Use the definition of the derivative to find f'(x) for f(x) = 3x + 2.
5. Find the derivative of f(x) = x² - 5x using the definition of the derivative.
6. Which of the following expressions represents the definition of the derivative?
lim (h→0) [f(x) - f(x+h)] / h
lim (h→0) [f(x+h) - f(x)] / h
lim (x→0) [f(x+h) - f(x)] / x
lim (h→inf) [f(x+h) - f(x)] / h
7. The derivative of a constant function is always zero.
True
False