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Let be a function such that and . Let . Then, consider the following statements: Statement I: …

Mathematics20251 markMCQ
Let $f(x)$ be a function such that $f'(x) = g(x)$ and $f''(x) = -f(x)$. Let $h(x) = \{f(x)\}^2 + \{g(x)\}^2$. Then, consider the following statements: Statement I: $h'(2024) = 0$. Statement II: $h(2) = h\left(\frac{1}{2}\right)$ Which of the statements given above is/are correct?
  • (a)I only.
  • (b)II only
  • (c)Both I and II
  • (d)Neither I nor II.

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Continuity, Differentiability and Differentiation

From ISC 2025 Practice Mathematics, question 27.