Rolle’s Theorem Calculator
What is Rolle’s Theorem
Rolle’s Theorem is a fundamental theorem in calculus that states: if a function f(x) is continuous on [a,b], differentiable on (a,b), and f(a) = f(b), then there exists at least one point c in (a,b) where the derivative f'(c) = 0. This theorem is crucial in proving the Mean Value Theorem and has important applications in function analysis and optimization.
How to Use Rolle’s Theorem Calculator
Step 1: Enter your function in the input field using standard mathematical notation. For example, type “x^2 – 4x + 3” for the function f(x) = x² – 4x + 3.
Step 2: Input the left endpoint (a) of your interval in the corresponding field. This should be a real number.
Step 3: Input the right endpoint (b) of your interval. Ensure that b is greater than a.
Step 4: Click the calculate button to obtain results. The calculator will:
- Verify if f(a) equals f(b)
- Check if the function satisfies Rolle’s Theorem conditions
- Find critical points where f'(x) = 0 within the interval
Step 5: Review the results displayed in the result section, which includes:
- Values of f(a) and f(b)
- Critical points found in the interval
- Detailed explanation of the theorem’s application