Question 4
Differentiate, with respect to x, y = 3x2 + 4x β 1, from first principles.
Observation
The Chief Examiner observed that majority of the Candidates that attempted this question got it right.
They were able to express y + πΏπ¦=3(π₯+πΏπ₯)2+4(π₯+πΏπ₯)β1 after which they simplified
and found πΏπ¦ to be πΏπ¦=6π₯πΏπ₯+3(πΏπ₯)2+4πΏπ₯. Next, they divided all through by πΏπ₯ to obtain
πΏπ¦⁄πΏπ₯=6π₯+3(πΏπ₯)+4 after which they took the limit of both sides as πΏπ₯β0 and obtained
πΏπ¦⁄πΏπ₯=6π₯+4.