Derivative by Definition Worksheet
Practice problems for understanding and calculating derivatives using the limit definition.
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Derivative by Definition
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Read each question carefully and show all your work. Use the definition of the derivative to solve each problem.
1. The derivative of a function f(x) with respect to x is given by the limit: f'(x) = lim (h→0) [ ].
2. The derivative represents the of the tangent line to the curve at a given point.
1. Using the definition of the derivative, find f'(x) for the function f(x) = 3x + 2.
2. Calculate the derivative of f(x) = x² using the limit definition.
1. The derivative of a constant function is always zero.
True
False
2. If a function is differentiable at a point, it must also be continuous at that point.
True
False
1. Which of the following is the correct limit definition of the derivative?
lim (h→0) [f(x+h) - f(x)] / x
lim (h→0) [f(x+h) - f(x)] / h
lim (x→0) [f(x+h) - f(x)] / h
lim (h→∞) [f(x+h) - f(x)] / h
3. Find the derivative of f(x) = 1/x using the definition of the derivative.
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