noelwolfe said:9/2=tan(x)
and then I'm not sure what to do with 9/2?
A horizontal tangent is a line that is parallel to the x-axis and touches a curve at a specific point. This means that the slope of the tangent line is equal to 0 at that point.
Finding horizontal tangents can help us identify critical points on a curve, which can be useful in optimization problems. It can also help us determine the concavity of a curve and identify points of inflection.
To find horizontal tangents on an interval, we need to first find the derivative of the function. Then, we set the derivative equal to 0 and solve for the x-values. These x-values will be the points where the tangent line is horizontal. We can then check if these points fall within the given interval.
Yes, a function can have more than one horizontal tangent on an interval. This can happen if the function has multiple points where the derivative is equal to 0 within the given interval.
Yes, there are other methods such as using the second derivative test or graphing the function to visually identify points where the tangent line is horizontal. However, the most common and efficient method is to find the points where the derivative is equal to 0.