True or False: If f'(c)=0 and f(c) is not a local maximum, then f(c) is a local minimum?

Justify your answer.True or False: If f'(c)=0 and f(c) is not a local maximum, then f(c) is a local minimum?
Hi,





That's FALSE.





While if f'(c)=0 and f(c) is not a local maximum, then f(c) could be a local minimum, it could also be a point where a graph goes from concave down to concave up like f(0) on f(x) = x鲁. Here f'(x) = 3x虏 and f'(0) = 3(0)虏 = 0, but the point is neither a maximum nor a minimum - it's a point of inflection.





I hope that helps!! :-)True or False: If f'(c)=0 and f(c) is not a local maximum, then f(c) is a local minimum?
false