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Attempt following question by selecting a choice to answer.
Use Rolle's Theorem to determine the value of
such that ′ () = 0,
if () = ( - ) ( - )
are positive integers in the interval [, ].ff ff
Step 1: () = ( - ) ( - )[Write the function.]
Step 2: () = 0 and () = 0[Find () and ().]
Step 3: Since () = () = 0, () is continuous in [, ] and differentiable in (, ), Rolle's Theorem is applicable.
Step 4: There exists a number in (, ) such that ′() = 0.
Step 5: ′() = 0 ( - )( - ) - 1 + ( - )( - ) - 1 = 0[Equate ′() to zero.]
Step 6: = -
Step 7: = -
Step 8: - = - + , so = [Solve for .]
Step 9: So, the derivative of the function is zero at = in the interval [, ].