Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Applications Of Derivatives · Assertion Reason1 Marksassertion_reason

Class 12 Maths · Applications Of Derivatives · Assertion Reason #27

Assertion: The function x²−x is strictly increasing on (1/2,∞). Reason: At an interior local extremum of a differentiable function, the first derivative is zero.
Derivative sign chart (ar 5)
Derivative sign chart (ar 5)

✅ Step-by-Step Solution

Final Answer: Option (B): Both A and R are true, but R does not correctly explain A.
  1. The derivative 2x−1 is positive for x>1/2. R is Fermat’s necessary condition and does not explain the positive derivative on this interval.

Master Chapter 6: Applications Of Derivatives

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Derivatives.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
Assertion: The maximum value of ln x/x on [2,∞) is 1/e. Reason: If a…
Next Question →
Water drains at 2 cm³/s from the bottom of an inverted conical tank…

More Practice Questions in Applications Of Derivatives

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Applications Of Derivatives

Class 12 Applications Of Derivatives · Mcq Single Correct
Find the maximal open interval on which f(x)=x²e^(−x) has positive derivative.
Class 12 Applications Of Derivatives · Mcq Single Correct
For f(x)=x²−4x+6, identify the maximal open interval where f′(x)>0.
Class 12 Applications Of Derivatives · Mcq Single Correct
For x>0, at which x is f(x)=x^x stationary?
Class 12 Applications Of Derivatives · Mcq Single Correct
Find the maximum value of (1/x)^x for x>0.
Class 12 Applications Of Derivatives · Mcq Single Correct
Find the maximum of [x(x−1)+1]^(1/3) on 0≤x≤1.
Class 12 Applications Of Derivatives · Mcq Single Correct
A trapezium area model is A(x)=(10+x)√(100−x²) cm² for 0≤x≤10. Find its maximum.