Class 12 Applications Of Derivatives · Short Answer2 Marksmonotonicity
Class 12 Maths · Applications Of Derivatives · Short Answer #50
Show that f(x)=x/3+3/x is strictly decreasing on each of the intervals (−3,0) and (0,3).
✅ Step-by-Step Solution
Final Answer: Strictly decreasing separately on (−3,0) and (0,3).
- f′=1/3−3/x²=(x²−9)/(3x²), x≠0.
- For 0<|x|<3 its numerator is negative and denominator positive.
- Hence f′<0 on each stated interval, proving strict decrease separately.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] f′=1/3−3/x²=(x²−9)/(3x²), x≠0.
- [1 mark] For 0<|x|<3 its numerator is negative and denominator positive.
- [0.5 marks] Hence f′<0 on each stated interval, proving strict decrease separately.
Master Chapter 6: Applications Of Derivatives
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Derivatives.
← Previous Question
Show that f(x)=(x−1)e^x+1 is strictly increasing for x>0.
Next Question →Is there a nonzero real b for which f(x)=b/x is strictly increasing…
More Practice Questions in Applications Of Derivatives
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.