Let f(x) be a function such that f^ (x)=g(x) and f^ (x)=-f(x) . Let h(x)= f(x) ^2+ g(x) ^2 . Then consider the following statements : 1. h^ (3)=0 2. h(1)=h(2) Which of the statements given above is/are correct?

Step-by-step solution

aligned & h(x)= f(x) ^2+ g(x) ^2 & = f(x) ^2+ f^ (x) ^2 & h^ (x)=2 f(x) f^ (x)+2 f^ (x) f^ (x) & =2 f(x) f^ (x)-2 f(x) f^ (x)=0 & h' (x)=0 & h^ (3)=0 aligned Statement 1 is correct. aligned & h^ (x)=0 h(x)= constant function & h(1)=f(2) aligned Statement 2 is correct.