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Question
Using the Rolle’s theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions:
`f(x)` = x2 – x, x ∈ [0, 1]
Solution
f(0) = 0, f(1) = 0
⇒ f(0) = f(1) = 0
f(x) is continuous on [0, 1]
f(x) is differentiable on (0, 1)
Now, f'(x) = 2x – 1
Since, the tangent is parallel to x-axis then
f'(x) = 0
⇒ 2x – 1 = 0
x = `x/3` ∈ (0, 1)
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