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Attempt following question by selecting a choice to answer. c
Use Rolle's Theorem to determine the value of c such that f ′ (c) = 0, if f(x) = xx+5 in the interval [ 5, 0].fff cccA. c103B. c 13 C. c 103D. c 5 E. c0 cc
C
Step 1: f(x) = xx+5[Write the function.]
Step 2: f( 5) = ( 5)5+5 = 0[Find f( 5).]
Step 3: f(0) = 0[Find f(0).]
Step 4: Since f(x) is continuous in [ 5, 0] and differentiable in ( 5, 0) also f( 5) = f(0) = 0, Rolle's Theorem is applicable.
Step 5: There exists a number c in ( 5, 0) such that f ′(c) = 0.
Step 6: f ′(c) = 3c+102c+5[Find f ′(c).]
Step 7: 3c+102c+5 = 0[Equate f ′(c) to zero.]
Step 8: c =  103, which lies between the interval ( 5, 0)[Solve for c.]
Step 9: So, the derivative of the function is zero at c =  103 in the interval [ 5, 0].

