how we verify rolle's theorem
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You found the points where f(x)=0, not where the derivative is zero. Rolle's theorem. If f is continuous on [a,b] and differentiable on (a,b), with f(a)=f(b), then there exists c∈(a,b) such that f(c)=0.
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To verify Rolle's Theorem. A piece of plywood, wires of different lengths, white paper, sketch pen. 4. Take two straight wires of the same lengthsi by and fix them in such way that they are perpendicular to x-axis at the points A and B and meeting the curve at the points C and D
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