If \(\displaystyle\frac{d}{dx}[ax^3+ ax^2 + ax + 1] = 9x^2 + 6x +3\), then \(a\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3
Differentiating term by term (a is a constant):
\(\displaystyle \frac{d}{dx}[ax^3 + ax^2 + ax + 1] = 3ax^2 + 2ax + a\)
This must equal \(9x^2 + 6x + 3\) for every x, so by comparing coefficients:
\(3a = 9,\quad 2a = 6,\quad a = 3\)
All three equations give \(a = 3\).