Question

If f(x) has the second order derivative at x = c such that f '(c) = 0 and f ''(c) > 0, then c is a point of _______________.

Answer 1

Second derivative test: Let f(x) be a function defined on an interval I and c ∈ I. Suppose f(x) be twice differentiable at x = c. Then, x = c is a point of local minima if f '(c) = 0 and f ''(c) > 0. In this case, f(c) is then the local minimum value of f(x).

So, if f(x) has the second order derivative at x = c such that f '(c) = 0 and f ''(c) > 0, then c is a point of local minima.


If f(x) has the second order derivative at x = c such that f '(c) = 0 and f ''(c) > 0, then c is a point of ___local minima___.