Let $$g\left( x \right) = \log f\left( x \right)$$ where $$f(x)$$ is twice differentible positive function on $$\left( {0,\infty } \right)$$ such that $$f(x+1)=x f(x)$$. Then, for $$N=1, 2, 3, ..........$$
$$g''\left( {N + {1 \over 2}} \right) - g''\left( {{1 \over 2}} \right) = $$
Let $$\,\,\,$$$$f\left( x \right) = 2 + \cos x$$ for all real $$X$$.
STATEMENT - 1: for eachreal $$t$$, there exists a point $$c$$ in $$\left[ {t,t + \pi } \right]$$ such that $$f'\left( c \right) = 0$$ because
STATEMENT - 2: $$f\left( t \right) = f\left( {t + 2\pi } \right)$$ for each real $$t$$.
A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1