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NDA 2 2024 Maths, question 96

Topic: Differential calculus

Passage · Q95 to Q96

Let f:(−1,1)→Rf:(-1,1)\to R be a differentiable function with f(0)=−1f(0)=-1 and f′(0)=1f'(0)=1. Let h(x)=f(2f(x)+2)h(x)=f(2f(x)+2) and g(x)=(h(x))2g(x)=(h(x))^{2}.

Q96

What is g′(0)g'(0) equal to?

  1. (a) −4-4Correct answer
  2. (b) −2-2
  3. (c) 00
  4. (d) 44

Solution.

Answer: (a) −4-4

  1. First h(0)=f(2f(0)+2)=f(0)=−1 and h′(0)=2.
  2. Differentiating g=h² gives g′(0)=2h(0)h′(0)=2(−1)(2)=−4.