Q72.The sum of all the local minimum values of the twice differentiable function f : R →R defined by ′′(2) x + f ′′(1) is: f(x) = x3 −3x2 −3f 2 (1) −22 (2) 5 (3) −27 (4) 0
What This Question Tests
This question involves finding local minimum values of a function where the second derivative itself depends on function values. It requires careful calculation of derivatives, solving for critical points, and using the second derivative test, while also solving for f''(1) and f''(2).
Concepts Tested
Formulas Used
f'(x) = 0 for critical points
f''(x) > 0 for local minimum
📚 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
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
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
- Local minima of a function
- Year
- 2021
- Shift
- 20 Jul Shift 2
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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