Question
Download Solution PDFComprehension
Direction : Consider the following for the items that follow :
Let f : (-1, 1) → R be a differentiable function with f(0) = -1 and f’(0) = 1 Let h(x) = f(2f(x) +2) and g(x) = (h(x))2.
What is h’(0) equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Let f: (–1, 1)→ R be a differentiable function with f(0) = –1 and f'(0) = 1
⇒ h(x) = f(2f(x) + 2)
⇒ h'(x) = f'(2f(x) + 2)2f'(x)
⇒ h'(0) = f'(2f(0) + 2).2f'(0)
= f'(–2 + 2).2(1)
= f'(0).2 = (1).2 = 2
∴ Option (d) is correct.
Last updated on May 30, 2025
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