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.
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.
Hope this information will clear your doubts about topic.
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