A stationary point is a point on a curve where the gradient is equal to zero. This means that the curve is neither increasing nor decreasing at that point.
To find the stationary points of this function within the given interval, you would need to use the first derivative test. This involves finding the derivative of the function, setting it equal to zero, and solving for the values of x that make the derivative equal to zero. These values will be your stationary points.
Stationary points are important because they can help us identify maximum and minimum points on a curve. They also provide information about the rate of change of the function at that point, as well as the concavity of the curve.
Yes, a function can have multiple stationary points. This means that the gradient of the curve is equal to zero at different points along the curve.
To determine if a stationary point is a maximum or minimum, you would need to use the second derivative test. This involves finding the second derivative of the function and plugging in the x-value of the stationary point. If the second derivative is positive, the point is a minimum. If the second derivative is negative, the point is a maximum.