### Question 3

If f’’(x) = 2, f’(1) = 0 and f(0) = -8, find f(x).

### Observation

Although the question was quite popular among the candidates, majority of them were reported not to perform well in it. They displayed poor knowledge of integration.

Candidates were expected to integrate f’’(x) = 2 with respect to x to obtain f’(x) = 2x + c. it was given that f’(1) = 0. This implied that 2x + c = 0 when x = 1. i.e. 2(1) + c = 0. This gave c = -2. Hence, f’(x) = 2x – 2. Integrating f’(x) with respect to x gave f(x) = x2 – 2x + p. But f(0) = -8, this implied that p = -8. Therefore, the required equation was f(x) = x2 -2x – 8.