Consider the following statements: 1. f(x)= x is increasing in (0, ) 2. g(x)=e^x+e^ 1 x is decreasing in (0, ) Which of the statements given above is/are correct?

Step-by-step solution

f(x)= x f^ (x)= 1 x for x (0, ), f^ (x) 0 f(x) is increasing in (0, )g(x)=e^x+e^ 1 / x g^ (x)=e^x-e^ 1 / x ( 1 x^2 ) when x 1, g^ (x) 0 at x=1, g^ (x)=0 at x 1, g^ (x) 0 in (0, ), g(x) is neither continuously increasing nor decreasing. Only 1 is correct.