Question

Let b be a nonzero real number. Suppose f:R→R is a differentiable function such that (0) = 1. If the derivative f′ of f satisfies the equation f'(x) = f(x)/(b² + x²) for all x ∈ R, then which of the following statements is/are TRUE? 

(A) If b > 0, then f is an increasing function 

(B) If b < 0, then f is a decreasing function 

(C) (x) (−x)=1 for all x ∈ R 

(D) (x)−(−x)=0 for all x ∈ R

Answer 1

(A) If b > 0, then f is an increasing function,

(C) (x) (−x) = 1 for all x ∈ R

f(x) is increasing for all x ∈ R