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Attempt following question by selecting a choice to answer. B
Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = x(x  1) in the interval [0, 1].BBBB BBBBA. B 12B. B12C. B0 D. B1 E. B 1 BB
B
Step 1: f(x) = x(x  1)[Write the function.]
Step 2: f(0) = 0[Find f(0).]
Step 3: f(1) = 1(1  1) = 0[Find f(1).]
Step 4: Since f(x) is continuous in [0, 1] and differentiable in (0, 1) also f(0) = f(1) = 0, Rolle's Theorem is applicable.
Step 5: There exists a number c in (0, 1) such that f ′(c) = 0.
Step 6: f ′(c) = 2c  1[Find f ′(c).]
Step 7: 2c  1 = 0[Equate f ′(c) to zero.]
Step 8: c = 12, which lies between the interval (0, 1)[Solve for c.]
Step 9: So, the derivative of the function is zero at c = 12 in the interval [0, 1].

