At a critical point x=c of a twice differentiable function f, it is given that f′(c)=0 and f′′(c)<0. Which of the following statements is correct about x=c?
a) The nature of x=c cannot be determined from the given data
b) f(c) is a local minimum
c) f(c) is a local maximum
d) x=c is a point of inflection