Ques 6

Dear Student
As f (x) is a polynomial function. Hence, it is continuous in the closed interval [0,1].

f '(x) = 2(a+b)x + c. Hence, the function is differentiable in the open interval (0,1).
From L.M.V.T. ;
f ' (c) = [f (b) - f (a)]/ b - a
         = (a + b + c + d - d)                as b=1 & a = 1
         = a + b + c
c =  ( a + b + c)dx

 c  = ax + bx + cx + k        where, k is the Constant of integration.
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  • 0
As f (x) is a polynomial function. Hence, it is continuous in the closed interval [0,1].
f '(x) = 2(a+b) + c. Hence, the function is differentiable in the open interval (0,1).
From L.M.V.T. ;
f ' (c) = [f (b) - f (a)]/ b - a
         = (a + b + c + d - d)
         = a + b + c
c = integration of ( a + b + c)
   = ax + bx + cx + C        where, C is the Constant of integration.
  • 0
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