Doubt on inflection point conditions

Question

Consider the question:-

Give an example of a function such that:-

1. $f(x)$ is continuous and differentiable at $x=a$
2. First derivative of $f(x)$ is $0$ at $x=a$
3. First derivative of $f(x)$ has same sign(positive or negative) on both sides of $x=a$
4. $x=a$ is not an inflection point

The first 3 conditions don’t satisfy all conditions to be an inflection point yet I am unable to find a function to the above conditions.

Please help me in finding such a function. If such a function doesn’t exist, then are the the first 3 conditions enough to declare $x=a$ an inflection point?

Answer 1

The only such function would be $y=c$, where $c\in\mathbb{R}$ is some constant. All the other functions can't possibly satisfy 2nd and 3rd condition without there being an inflection point at $x=a$.