Class 12 Continuity And Differentiability · Short Answer2 Markssecond_derivatives
Class 12 Maths · Continuity And Differentiability · Short Answer #58
For y=√(ax+b) on any open interval where ax+b>0, prove yy″+(y′)²=0.
✅ Step-by-Step Solution
Final Answer: yy″+(y′)²=0
- Squaring gives y²=ax+b. Differentiation yields 2yy′=a.
- Differentiate again by the product rule: 2[(y′)²+yy″]=0.
- Divide by 2 to obtain yy″+(y′)²=0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Squaring gives y²=ax+b. Differentiation yields 2yy′=a.
- [1 mark] Differentiate again by the product rule: 2[(y′)²+yy″]=0.
- [0.5 marks] Divide by 2 to obtain yy″+(y′)²=0.
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