Let p(x) and q(x) be differentiable functions such that p(x)>0 and q(x)>0 for all x. At x=c it is known that p′(c)>0 and q′(c)<0. For the product f(x)=p(x)q(x), which statement about f′(c) must be true?
a) f′(c)>0
b) f′(c)=0
c) The sign of f′(c) depends on the relative magnitudes of p(c), q(c), p′(c), and q′(c).
d) f′(c)<0