The GATE Grind

GATE Calculus and Optimization: Taylor series, maxima and minima, single-variable optimization – Previous Year Questions

6 GATE previous year questions on Taylor series, maxima and minima, single-variable optimization (Calculus and Optimization, Data Science and Artificial Intelligence) with answers and explanations, from every paper.

  1. GATE 2024 DA Q15 (1 mark, Multiple choice) – For any twice differentiable function f: R R, if at some x* R, f'(x*) = 0 and f''(x*) > 0, then the function f necessarily has a at x = x*.
  2. GATE 2024 DA Q50 (2 marks, Multiple select) – Consider the function f: R R where R is the set of all real numbers. f(x) = x44 - 2x33 - 3x22 + 1 Which of the following statements is/are TRUE?
  3. GATE 2025 DA Q14 (1 mark, Multiple choice) – Let f(x) = ex - e-x2, x R. Let f(k)(a) denote the kth derivative of f evaluated at a. What is the value of f(10)(0)? (Note: ! denotes factorial)
  4. GATE 2025 DA Q49 (2 marks, Multiple select) – Consider the function f(x) = x33 + 72x2 + 10x + 1332, x [-8, 0]. Which of the following statements is/are correct?
  5. GATE 2025 DA Q51 (2 marks, Multiple select) – Let f: R R be a twice-differentiable function and suppose its second derivative satisfies f''(x) > 0 for all x R. Which of the following statements…
  6. GATE 2026 DA Q27 (1 mark, Multiple select) – Let f(x) = x3 - 3x2 + 2 be a function defined on (-1, 3]. Which of the following statements is/are correct?