Q. 463.7( 3 Votes )

If f’(x) = x + b,

Answer :

Given f’(x) = x + b, f(1) = 5 and f(2) = 13


On integrating the given equation, we have



We know





Recall and




On substituting x = 1 in f(x), we get





….. (1)


On substituting x = 2 in f(x), we get



13 = 2 + 2b + c


13 – 2 = 2b + c


2b + c = 11 ….. (2)


By subtracting equation (1) from equation (2), we have





On substituting the value of b in equation (1), we get




c = –2


On substituting the values of b and c in f(x), we get




Thus,


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