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NDA 2024 Maths · Mathematics · Application of Derivatives · medium

The minimum value of f(x)=x^4-8x^2+3 is

Single correct option

The minimum value of f(x)=x4−8x2+3f(x)=x^4-8x^2+3 is
  1. A. 33
  2. B. −13-13
  3. C. −16-16
  4. D. −5-5
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Answer: (B) −13-13

f′(x)=4x3−16x=4x(x−2)(x+2)f'(x)=4x^3-16x=4x(x-2)(x+2), with critical points 0,±20,\pm2. At x=±2x=\pm2, f=16−32+3=−13f=16-32+3=-13 (minima), while f(0)=3f(0)=3 is a local maximum. Trap: 33 is the value at the local maximum, and −16-16 is x4−8x2x^4-8x^2 without the constant 3.
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