Let f(x) be a function such that its derovative f'(x) is continuous in [a, b] and differentiable in (a, b). Consider a function phi(x)=f(b)-f(x)-(b-x)f'(x)-(b-x)^(2)A. If Rolle's theorem is applicable to phi(x) on, [a,b], answer following questions. Let f(x)=x^(3)-3x+3, a=1 and b=1+h. If there exists c in (1,1+h) such that phi'(c)=0 and (f(1+h)-f(1))/(h^(2))=lambdac, then lambda=

Let f(x) be a function such that its derovative f'(x) is continuous in

1.	Let f(x) be a function such that its derovative f'(x) is continuous in [a, b] and differentiable in (a, b). Consider a function phi(x)=f(b)-f(x)-(b-x)f'(x)-(b-x)^(2)A. If Rolle's theorem is applicable to phi(x) on, [a,b], answer following questions. Let f(x)=x^(3)-3x+3, a=1 and b=1+h. If there exists c in (1,1+h) such that phi'(c)=0 and (f(1+h)-f(1))/(h^(2))=lambdac, then lambda=
Answer» `1//2` 2 3 does not exist Solution :`f(1+h)=f(1)+hf'(1)+(1)/(2)h^(2)f''(c)` `THEREFORE""f(1+h)=1+3h^(2)c` `therefore""(f(1+h)-f(1))/(h^(2))=3e` `therefore""lambda=3`

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