Mean Value Theorem Worksheet
A Grade 10 Math worksheet exploring the concepts and applications of the Mean Value Theorem in Calculus.
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Mean Value Theorem Worksheet
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Read each question carefully and provide clear, concise answers. Show all your work for full credit.
1. Which of the following conditions is NOT required for the Mean Value Theorem to apply to a function f(x) on a closed interval [a, b]?
f(x) is continuous on [a, b]
f(x) is differentiable on (a, b)
f(a) = f(b)
None of the above
2. The Mean Value Theorem states that if a function f is on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in (a, b) such that f'(c) = .
3. If a function is continuous on [a, b] but not differentiable on (a, b), the Mean Value Theorem cannot be applied.
True
False
4. Consider the function f(x) = x^2 on the interval [0, 2]. Find all values of c that satisfy the conclusion of the Mean Value Theorem.
5. The graph below shows a function f(x) on the interval [a, b]. Sketch the secant line connecting (a, f(a)) and (b, f(b)). Then, sketch a tangent line parallel to the secant line, indicating the point 'c' where f'(c) equals the slope of the secant line.