GATE 2025 ST – Question 36

Calculus · Single Variable Calculus · 2 marks · Multiple choice

1. Some nonconstant f∈F satisfies |f(x)−f(y)|≤|x−y|² for all x,y.
2. Every f∈F and interior x₀ has distinct x₁,x₂ with secant slope f′(x₀).
3. If f′≥0 and f′ is zero at only two distinct points, f is strictly increasing.
4. A derivative may skip a value lying strictly between two of its values.

Practise this question in The GATE Grind →

More Single Variable Calculus questions

• GATE 2024 ST Q47 – Continuous f:[−2,2]→ℝ satisfies which statements?
• GATE 2023 ST Q43 – Let g(x)=f(x)+f(2−x) on [0,2],where f is continuous on [0,2] and twice differentiable…
• GATE 2022 ST Q50 – Which real functions are uniformly continuous on [0,∞)?
• GATE 2021 ST Q36 – Define f:ℝ→ℝ by f(x)=x³sin x if x=0 or x is irrational,and f(p/q)=1/q³ for nonzero reduced…
• GATE 2021 ST Q37 – For f:[0,∞)→ℝ,which statement is true?
• GATE 2021 ST Q38 – A differentiable f:ℝ→ℝ satisfies f(0)=0 and f′(x)+2f(x)>0 for all x. Which holds?

All Single Variable Calculus questions →