Derivative by Definition Worksheet
Grade 12 Calculus worksheet focusing on understanding and applying the derivative definition to find derivatives of various functions.
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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: f'(x) = lim (h→0) [f(x + h) - f(x)] / h to solve the problems.
1. Find the derivative of f(x) = 3x + 2 using the definition of the derivative.
2. Determine the derivative of g(x) = x² - 5x + 1 by applying the limit definition.
3. The derivative of a function at a point represents the of the tangent line to the function's graph at that point.
4. The process of finding the derivative is called .
5. The limit in the definition of the derivative is taken as h approaches .
6. Which of the following is the correct definition of the derivative f'(x)?
lim (h→0) [f(x) - f(x + h)] / h
lim (h→0) [f(x + h) + f(x)] / h
lim (h→0) [f(x + h) - f(x)] / h
lim (h→0) [f(x) - f(h)] / x
7. Find the derivative of h(x) = 1/x using the definition of the derivative.
8. The derivative of a constant function is always zero.
True
False