COMEDK · Maths · 27. Application of Derivatives
For a given curve \(y=2 x-x^2\), when \(x\) increases at the rate of 3 units/sec, then how does the slope of the curve change?
- A Increasing at 3 units/sec
- B Decreasing at 6 units/sec
- C Decreasing at 3 units/sec
- D Increasing at 6 units/sec
Answer & Solution
Correct Answer
(B) Decreasing at 6 units/sec
Step-by-step Solution
Detailed explanation
The equation of the curve is given by \(y = 2x - x^2\). The slope of the curve at any point \(x\) is given by \(m = \dfrac{dy}{dx} = 2 - 2x\). To find the rate of change of the slope with respect to time \(t\), we differentiate \(m\) with respect to \(t\) using the chain rule:…
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