Let f be the function with derivative given by f′(x)=x2−a2=(x−a)(x+a), where a is a positive constant. Which of the following statements is true?
A) f is decreasing for −a B) f is decreasing for x<−a and x>a because f′(x)<0 for x<−a and x>a.
C) f is decreasing for x<0 because f′(x)<0 for x<0.
D) f is decreasing for x<0 because f′′(x)<0 for x<0.