mathmike said:wouldnt f(-3) = -3 + 9 / (-3) = -3 -3 = -6
A quick local max/min question is a type of problem in calculus where you are asked to find the maximum or minimum value of a function within a specific interval. This can be done by finding the critical points of the function and evaluating them within the given interval.
To find the critical points of a function, you need to take the derivative of the function and set it equal to zero. Solve for the variable to find the critical points. These points represent where the slope of the function is equal to zero, which can indicate a potential maximum or minimum value.
A local max/min is the highest or lowest point within a specific interval, while a global max/min is the highest or lowest point over the entire domain of the function. A function can have multiple local max/min points, but only one global max/min point.
You can determine if a critical point is a local max/min by using the first or second derivative test. The first derivative test involves evaluating the sign of the first derivative on either side of the critical point. If the sign changes from positive to negative, then the critical point is a local maximum, and if the sign changes from negative to positive, then the critical point is a local minimum. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, then the critical point is a local minimum, and if it is negative, then the critical point is a local maximum.
Yes, local max/min problems have many real-world applications, especially in fields such as economics and physics. For example, in economics, local max/min problems can be used to determine the optimal production level for a company to maximize profits. In physics, they can be used to find the path of a projectile to reach the highest point or the shortest path between two points.