COMEDK · Maths · 27. Application of Derivatives
The turning point of the function \(y=\dfrac{a x-b}{(x-1)(x-4)}\) at the point \(P(2,-1)\) is
- A a maximum
- B both maximum and a minimum
- C a minimum
- D neither a maximum nor a minimum
Answer & Solution
Correct Answer
(A) a maximum
Step-by-step Solution
Detailed explanation
Given the function \(y = \dfrac{ax - b}{(x - 1)(x - 4)}\). Since the point \(P(2, -1)\) lies on the curve, we substitute \(x = 2\) and \(y = -1\): \(-1 = \dfrac{2a - b}{(2 - 1)(2 - 4)} = \dfrac{2a - b}{1 \times (-2)} = \dfrac{2a - b}{-2}\) \(2 = 2a - b \Rightarrow b = 2a - 2\)…
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