GATE Engineering Mathematics: Calculus: Maxima and minima – Previous Year Questions

8 GATE previous year questions on Calculus: Maxima and minima (Engineering Mathematics, Electrical Engineering) with answers and explanations, from every paper.

1. GATE 2016 EE Q11 (1 mark, Numerical answer) – The maximum value attained by the function f(x) = x(x - 1)(x - 2) in the interval [1, 2] is .
2. GATE 2018 EE Q53 (2 marks, Numerical answer) – Let f(x)=3x3-7x2+5x+6. The maximum value of f(x) over the interval [0,2] is (up to 1 decimal place).
3. GATE 2020 EE Q36 (2 marks, Multiple choice) – For real numbers, x and y, with y=3x2+3x+1, the maximum and minimum value of y for x[-2,0] are respectively,
4. GATE 2021 EE Q13 (1 mark, Multiple choice) – Let f(x) be a real-valued function such that f'(x 0)=0 for some x 0(0,1), and f''(x)>0 for all x(0,1). Then f(x) has
5. GATE 2022 EE Q41 (2 marks, Multiple choice) – Let f(x)= 0xet(t-1)(t-2)\,dt. Then f(x) decreases in the interval
6. GATE 2023 EE Q42 (2 marks, Multiple select) – Consider the following equation in a 2-D real-space. x 1 p+ x 2 p=1for p>0 Which of the following statement(s) is/are true.
7. GATE 2024 EE Q43 (2 marks, Multiple select) – Let f(t) be a real-valued function whose second derivative is positive for -<t<. Which of the following statements is/are always true?
8. GATE 2025 EE Q11 (1 mark, Multiple choice) – Consider the set S of points (x,y) R2 which minimize the real valued function f(x,y)=(x+y-1)2+(x+y)2 Which of the following statements is true about…