Question

True or false, if f ′(x)=0, then x must be an inflection point.

A) True
B) False

Answer 1

False. If f′(x)=0, x must be a critical point of the function f(x), but it doesn't necessarily mean that x is an inflection point. Therefore, the given statement is False

Step-by-step explanation:

False

If f′(x)=0, x must be a critical point of the function f(x), but it doesn't necessarily mean that x is an inflection point.

An inflection point is a point on the graph where the concavity changes.

For example, the function f(x) = x^3 has f′(x) = 0 at x = 0, but it is not an inflection point. The graph of this function is concave up on both sides of x = 0.