Let F(x) = X^2 + Xg'(1) + G\"(2) And G(x) = X^2 + Xf'(2) + F\"(3) . Then

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIIMathematicsHigher Order DerivativesQuestionLet f(x)=x2+xg′(1)+g′′(2) and g(x)=x2+xf′(2)+f′′(3). Then
  1. f′(1)=4+f′(2)
  2. g′(2)=8+g′(1)
  3. g′′(2)+f′′(3)=4
  4. all of these
Ag′′(2)+f′′(3)=4Bf′(1)=4+f′(2)Cg′(2)=8+g′(1)Dall of theseOpen in AppSolutionVerified by Toppr

f(x)=x2+xg′(1)+g′′(2)g(x)=x2+xf′(2)+f′′(3)Differentiating both the equations, we getf′(x)=2x+g′(1) and g′(x)=2x+f′(2)..............(1)Putting x=1 in eqn (1), we getf′(1)=2+g′(1) and g′(1)=2+f′(2)Then, f′(1)=4+f′(2)Putting x=2 in eqn (1), we getf′(2)=4+g′(1) and g′(2)=4+f′(2)g′(2)=4+4+g′(1)Then, g′(2)=8+g′(1)Differentiate eqn (1) w.r.t.x, we get,f′′(x)=2 and g′′(x)=2 for all xf′′(3)=2 and g′′(2)=2g′′(2)+f′′(3)=2+2=4

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