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The best approximation of the minimum value attained by e–x sin (100 x) for x > 0 is ______.
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- 0.9844
- 1.9844
- 11.91844
- None of these
Correct Option: A
f(x) = e– x sin(100x)
f '(x) = – e– xsin(100x) + e– xcos(100x) × 100
for minima f '(x) = 0
tan(100 x) = 100
| x = | tan-1(100) = 0.0156 | |
| 100 |
f(x) = e– 0.0156 sin(100 × 0.0156) = 0.9844
