Saved Bookmarks
| 1. |
For the given curve: y = 2x – x2, when x increases at the rate of 3 units/sec, then how the slope of curve changes?1. Increasing, at 6 units/sec2. decreasing, at 6 units/sec3. Increasing, at 3 units/sec4. decreasing, at 3 units/sec |
|
Answer» Correct Answer - Option 2 : decreasing, at 6 units/sec Concept: Rate of change of 'x' is given by \(\rm \frac {dx}{dt}\)
Calculation: Given that, y = 2x – x2 and \(\rm \frac {dx}{dt}\) = 3 units/sec Then, the slope of the curve, \(\rm \frac {dy}{dx}\) = 2 - 2x = m ⇒\(\rm \frac {dm}{dt}\) = 0 - 2 × \(\rm \frac {dx}{dt}\) = -2(3) = -6 units per second Hence, the slope of the curve is decreasing at the rate of 6 units per second when x is increasing at the rate of 3 units per second. Hence, option (2) is correct. |
|