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ফাংশন f(x) = x2 + 2x - 5 কত ব্যবধানে যথাযথভাবে বৃদ্ধি পাচ্ছে:

  1. (-∞, -1)
  2. [-1, ∞)
  3. (-∞, -1]
  4. (-1, ∞)

Answer (Detailed Solution Below)

Option 4 : (-1, ∞)
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Detailed Solution

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ধারণা:

একটি ফাংশনের জন্য y = f(x):

  • স্থানীয় ম্যাক্সিমা বা মিনিমার বিন্দুতে, f'(x) = 0।
  • যেসব অঞ্চলে f(x) বাড়ছে, f'(x) > 0।
  • যেসব অঞ্চলে f(x) কমছে, f'(x) < 0।

গণনা:

ফাংশন f(x) = x2 + 2x - 5 যথাযথভাবে বৃদ্ধি করার জন্য, f'(x) > 0।

⇒ f'(x) = 2x + 2 > 0

⇒ x > -1

⇒ x ∈ (-1, ∞)

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