Question

Let f and g be two function with f" and g" existing everywhere. If f(x)g(x)=2 for all x and f'(x)g'(x)is not 0.Then f"(x)/f'(x)=g"(x)/g'(x) ..
Has at least one real root
May have real roots
Has at most one real root
Has no real roots

Answer 1

@ganeshie8

Answer 2

f(x)g(x)=2 implies that g(x)=2/f(x).
f'(x)g'(x)!=0 implies f(x)!=c i.e. f(x) is not the constant function.

Answer 3

It is not a particularly hard question. There is no trick except those I provided above.

Answer 4

@hartnn

Answer 5

!= is not equal. If \(f'(x)g'(x)\neq0\) then \(f'(x)\neq0\) and \(g'(x)\neq0\). \(f'(x)\neq0\implies f(x)\neq c\)