Yes, it is possible for a function to have no critical points. This means that the function does not have any points where the derivative is equal to zero or undefined.
If a function has no critical points, it means that the function is either constantly increasing or constantly decreasing on its entire domain. This also means that the function does not have any local maximum or minimum points.
Yes, a continuous function can have no critical points. The continuity of a function does not guarantee the existence of critical points. A function can be continuous and still have a constant slope, resulting in no critical points.
To determine if a function has no critical points, you can take the derivative of the function and set it equal to zero. If the equation has no solutions or if the derivative is undefined for all values, then the function has no critical points.
Yes, it is possible for a function to have no critical points but still have a global maximum or minimum. This can occur if the function is bounded or has an asymptote, such as in the case of a rational function. In these cases, the function may have a global maximum or minimum, but no critical points.