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  1. GATE CS
  2. PYQs
  3. Engineering Mathematics

Find the minimum value of 3 - 4x + 2x^2.

GATE 1995 · Engineering Mathematics · Maxima Minima · easy

Answer: 1

  1. Write the function and differentiate: f(x) = 2x^2 - 4x + 3 (rewriting 3 - 4x + 2x^2). f'(x) = 4x - 4. Setting f'(x) = 0: 4x - 4 = 0 => x = 1.
  2. Confirm minimum via second derivative: f''(x) = 4 > 0, confirming x = 1 is a minimum.
  3. Evaluate the minimum value: f(1) = 2(1)^2 - 4(1) + 3 = 2 - 4 + 3 = 1.