Suppose that a function dX has the first derivative dX and s

Suppose that a function d(X) has the first derivative d\'(X) and second derivative d\"(X). Also suppose that the critical point for d(X) is x = 5, where d\'(5) = 0. If d\'(5) > 0, then there is a relative minimum for function d(X) at x = 5. True False

Solution

Its TRUE because for stationary point

a)if second derivative is POSITIVE for the given stationary point then MINIMUM lies at the stationary point

b)if second derivative is NEGATIVE for the given stationary point then MAXIMUM lies at the stationary point

c)if second derivative is ZERO for the given stationary point then it may or may not have EXTREME for that stationary point.