Further Mathematics Paper 2 WASSCE private candidates second series 2019

Question 4

Differentiate, with respect to x, y = 3x2 + 4x – 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 + 𝛿𝑦=3(π‘₯+𝛿π‘₯)2+4(π‘₯+𝛿π‘₯)βˆ’1 after which they simplified

and found 𝛿𝑦 to be 𝛿𝑦=6π‘₯𝛿π‘₯+3(𝛿π‘₯)2+4𝛿π‘₯. Next, they divided all through by 𝛿π‘₯ to obtain


𝛿𝑦𝛿π‘₯=6π‘₯+3(𝛿π‘₯)+4 after which they took the limit of both sides as 𝛿π‘₯β†’0 and obtained


𝛿𝑦𝛿π‘₯=6π‘₯+4.