Q80.The function f defined by f(x) = x3 −3x2 + 5x + 7 is: (1) Decreasing in R (2) Increasing in R (3) Increasing in (0, ∞) and decreasing in (−∞, 0) (4) Decreasing in (0, ∞) and increasing in (−∞, 0)
What This Question Tests
This question tests the fundamental concept of determining the monotonicity of a function by examining the sign of its first derivative, requiring knowledge of quadratic equation properties.
Concepts Tested
Formulas Used
f'(x) > 0 for increasing function
D = b^2 - 4ac for quadratic ax^2+bx+c
📚 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.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Monotonicity of functions
- Year
- 2017
- Shift
- 09 Apr Online
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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