ghostanime2001 said:for 1. don't i use inequality ? set the equation f(x) < 0 and solve for x if it can't be solved then u can conclude there are no points that can give me a negative tangent
When we talk about tangents in mathematics, we are referring to the slope of a line that touches a curve at a specific point. The slope of a tangent can be positive, negative, or zero. A non-negative tangent simply means that the slope is either positive or zero, but not negative.
In many applications of mathematics, such as optimization problems, it is important to know the direction of change at a specific point. By showing that the tangent is non-negative, we can determine that the function is increasing or staying constant at that point.
To determine if a tangent is non-negative, we need to find the derivative of the function at the given point. If the derivative is greater than or equal to zero, then the tangent is non-negative. If the derivative is negative, then the tangent is negative.
No, a tangent can only be either non-negative or negative at a given point. This is because the slope of a tangent is determined by the derivative of the function at that point, and the derivative can only have one value at a specific point.
Non-negative tangents can be useful in many real-world applications, such as determining the maximum or minimum value of a function, finding the best rate of change, or optimizing a process. By understanding the direction of change at a specific point, we can make informed decisions and solve problems more efficiently.