- #1
markosheehan
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whats the turning point of (1-lnx)², x>2 is it a minimum or maximum. can someone help me
A turning point is a point on a graph where the direction of the curve changes, from increasing to decreasing or vice versa.
To determine the location of a turning point, you need to find the x-value where the slope of the curve is equal to zero. This can be done by finding the derivative of the function and setting it equal to zero, then solving for x.
The nature of a turning point refers to whether the point is a local maximum or minimum. A local maximum is the highest point on a curve within a specific interval, while a local minimum is the lowest point on a curve within a specific interval.
To determine the nature of a turning point, you need to look at the second derivative of the function at that point. If the second derivative is positive, the turning point is a local minimum. If the second derivative is negative, the turning point is a local maximum. If the second derivative is zero, the nature of the turning point is indeterminate.
Determining the location and nature of turning points can help us understand the behavior of a function and identify important features such as maxima and minima. This information is useful in various fields such as economics, physics, and engineering, where the analysis of curves and functions is crucial in making accurate predictions and decisions.