Question Statement:
Consider the function
f(x) = {x2 for x < 0
x for x ≥ 0
where x is real. Which of the following statements is/are correct?
Options:
-
(A) The function is continuous for all x
-
(B) The derivative of the function is discontinuous at x = 0
-
(C) The derivative of the function is continuous at x = 1
-
(D) The function is discontinuous at x = 0
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2024 Q.45)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Structural Mechanics** under *Aerospace Structures* (2 Marks, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Structural Mechanics.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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