The following problem is a parabola so there is only one turning points so the answer is going to be: 2
No.
They cannot.
If the denominator is zero at some point, then the function is not defined at the corresponding points.
The turning points of a graph indicate where the function changes direction, signaling local maxima and minima. Specifically, a turning point corresponds to a change in the sign of the first derivative, which means the function is either increasing or decreasing before and after that point. Analyzing these points helps identify critical features of the function, such as the overall shape and behavior, which can be useful for optimization and understanding trends.
Yes, if no endpoints are defined.
No.
They cannot.
If the denominator is zero at some point, then the function is not defined at the corresponding points.
Yes. So long as the function has a value at the points in question, the function is considered defined.
Two.Two.Two.Two.
The turning points of a graph indicate where the function changes direction, signaling local maxima and minima. Specifically, a turning point corresponds to a change in the sign of the first derivative, which means the function is either increasing or decreasing before and after that point. Analyzing these points helps identify critical features of the function, such as the overall shape and behavior, which can be useful for optimization and understanding trends.
Differentiation, is often used to find the tangent of a curved graph. Each time you differentiate a function, you decrease the number of turning points in the graph, to a minimum of no turning points i.e. y = 3x. Differentiating to different orders is also used to find tangents, of tangents.
Yes, if no endpoints are defined.
The turning point of a graph is called a "critical point" or "extremum." In calculus, these points occur where the derivative of a function is zero or undefined, indicating a local maximum or minimum. At these points, the graph changes direction, which can represent peaks or valleys in the function's behavior.
The answer is all the points on the line defined by 25x - 12y = 1
That's how "function" is defined. If you have two points with the same x-coordinates, you have a "relation", but not a "function". A function is a special type of relation. The idea of a function is that, for every value of the independent variable (for example, "x"), the dependent variable (for example, "y") is uniquely defined. In other words, you can consider a function as a rule that assigns a y-value uniquely to every x-value.
{| |- | A line is defined by naming at least two points. It contains an infinite number of points, but two have to be identified. A line can also be defined by a single point and a direction. |}