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NDA 2 2024 Maths, question 73

Topic: Differential calculus

Q73

What is the minimum value of the function f(x)=log⁡10(x2+2x+11)f(x)=\log _{10}(x^{2}+2x+11)?

  1. (a) 00
  2. (b) 11Correct answer
  3. (c) 22
  4. (d) 1010

Solution.

Answer: (b) 11

  1. The logarithm is increasing, so minimise its argument.
  2. Since x²+2x+11=(x+1)²+10≥10, the minimum is log₁₀10=1, attained at x=−1.