(a) If {\y}=\sqrt{ {\a} x+ {\b}}, prove that {\y} ( { {\d}^2 {\y}}/{ {\d} x^2}) + ( { {\dy}}/{ {\d} x}) ^2=0. OR {\f}(x)={\\begin{array}{c}{\a\end{array} x+ {\b} {;}, 0 < x \leq 1 ; 2 x^2-x {;} ,1 < x < 2 is a differentiable function in (0,2), then find the values of a and b.

CBSE Class 12 Math 2023 Outside Delhi Set 1 Solved Paper

Question : 25 of 38

Marks: +1, -0

(a) If

{\y}=√{ {\a} x+ {\b}}

, prove that

{\y} (\;{ {\d}^2 {\y}}/{ {\d} x^2}) + (\;{ {\dy}}/{ {\d} x}) ^2=0

.

OR

{\f}(x)={\{\table {\a} x+ {\b} {;}, 0 < x ≤ 1 ; 2 x^2-x {;} ,1 < x < 2

is a differentiable function in

(0,2)

, then find the values of

a

and

b

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