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Let f:[0,1]toR (the set of all real numb...

Let `f:[0,1]toR` (the set of all real numbers ) be a function. Suppose the function f is twice differentiable,f(0)=f(1)=0 and satisfies
`f''(x)-2f'(x)+f(x)gee^(x),x in [0,1]` Consider the statements.
I. There exists some `x in R` such that, `f(x)+2x=2(1+x^(2))`
(II) There exists some `x in R` such that, 2f(x)+1=2x(1+x)

A

both P and Q are true

B

P is true and Q is false

C

P is false and Q is true

D

both P and Q are false

Text Solution

Verified by Experts

The correct Answer is:
C
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