Q73.Let the functions f : R →R and g : R →R be defined as : + 2, x < 0 x < 1 f(x) = and g(x) = {xx2, x ≥0 {x3,3x −2, x ≥1 Then, the number of points in R where (fog)(x) is NOT differentiable is equal to : (1) 3 (2) 1 (3) 0 (4) 2
What This Question Tests
This problem involves finding points of non-differentiability for a composite function made of two piecewise functions, requiring careful analysis of differentiability at critical points and across function definitions.
Concepts Tested
Formulas Used
Chain rule for differentiation
Left-hand and right-hand derivatives
Conditions for continuity and differentiability
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
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2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Differentiability of composite functions
- Year
- 2021
- Shift
- 16 Mar Shift 1
- Q Number
- Q73
- Type
- Multi concept
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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