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Question

It is given that the Rolle's theorem holds for the function f(x) = x3 + bx2 + cx, x [1, 2] at the point x = 43. Find the values of b and c.


Solution

As, the Rolle's theorem holds for the function f(x) = x3 + bx2 + cxx  [1, 2] at the point x = 43

So, f1=f213+b12+c1=23+b22+c21+b+c=8+4b+2c3b+c+7=0                   .....iAnd f'43=03432+2b43+c=0                As, f'x=3x2+2bx+c163+8b3+c=08b+3c+16=0                  .....iiii-i×3, we ge8b-9b+16-21=0-b-5=0b=-5Substituting b=-5 in i, we get3-5+c+7=0-15+c+7=0c=8

Mathematics
RD Sharma XII Vol 1 (2017)
Standard XII

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