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if f ‘(x) = x+ b ,f(1) = 5 , f(2) = 13 find f(x)

if f ‘(x) = x+ b ,f(1) = 5 , f(2) = 13 find f(x)

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question

f'(x) = x + b
\frac{df(x)}{dx} = x + b
df(x) = (x + b)dx
\int df(x) = \int (x + b)dx
f(x) = \frac{x^2}{2} + bx + c
f(1) = \frac{1^2}{2} + b(1) + c
5 = \frac{1}{2} + b + c
b + c = \frac{9}{2}….........(1)
f(2) = \frac{2^2}{2} + b(2) + c
13 = 2 + 2b + c
2b + c = 11.........(2)
(2) – (1)
b = 11 - \frac{9}{2} = \frac{13}{2}
c = \frac{9}{2} - \frac{13}{2} = -2
f(x) = \frac{x^2}{2} + \frac{13x}{2}-2

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