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If f^(prime)(x)=x+b ,f(1)=5,f(2)=13 , fi...

If `f^(prime)(x)=x+b ,f(1)=5,f(2)=13 ,` find `f(x)dot`

Text Solution

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`f'(x) = x+b`
`:. f(x) = int (x+b) dx`
`=>f(x) = x^2/2+bx+c`
Now, `f(1) = 5 => 1/2+b+c = 5 => b+c = 9/2 ->(1)`
`f(2) = 13 => 2+2b+c = 13 => 2b+c = 11 ->(2)`
`:. 2b+c - (b+c) = 11-9/2`
`=>b = 13/2`
`=> c = 9/2-13/2 = -2`
...
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