Class 12 Applications Of Derivatives · Short Answer2 Marksmonotonicity
Class 12 Maths · Applications Of Derivatives · Short Answer #49
Show that f(x)=(x−1)e^x+1 is strictly increasing for x>0.
✅ Step-by-Step Solution
Final Answer: Strictly increasing on (0,∞).
- By the product rule, f′=e^x+(x−1)e^x=xe^x.
- Both x and e^x are positive for x>0, so f′>0.
- The positive derivative proves strict increase on (0,∞).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] By the product rule, f′=e^x+(x−1)e^x=xe^x.
- [1 mark] Both x and e^x are positive for x>0, so f′>0.
- [0.5 marks] The positive derivative proves strict increase on (0,∞).
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