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MathCalculus

Rolle's Theorem: Verify f(x)=2x²−8x+6 on [1,3] and Find c

Verify Rolle's theorem for 2x²−8x+6 on [1,3] and find the only interior point with derivative zero.

Question

For f(x)=2x2−8x+6f(x)=2x^2-8x+6 on [1,3][1,3], verify every hypothesis of Rolle's theorem and find all c∈(1,3)c\in(1,3) for which f′(c)=0f'(c)=0.

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Evidence boundary

The function and interval come from OpenStax Checkpoint 4.14. All endpoint and derivative values are exact calculations from that function. No figure is needed.