absolute min/max
the highest and lowest point on a graph
Absolute minimum and maximum refer to the smallest and largest values a function attains over a given domain, respectively. Finding absolute minimum and maximum is important in optimization problems.
To find the absolute minimum and maximum of a function over a given interval, one needs to follow these steps:
1. Find critical points of the function: Critical points are points where the derivative of the function is equal to zero or undefined. To find the critical points, take the derivative of the function and set it equal to zero. Solve for the variable.
2. Identify endpoints of the interval: Endpoints are the values of the variable at the ends of the given interval.
3. Evaluate the function at the critical points and endpoints: Plug in the critical points and endpoints into the original function to obtain corresponding values of the function.
4. Compare the values obtained in step 3: The smallest value of the function is the absolute minimum, while the greatest value is the absolute maximum.
It is important to note that not all functions have absolute minimums and maximums. Some may have local or relative minimums and maximums instead.
More Answers:
Partial Differentiation: A Guide to Calculating Partial Derivatives of Functions with Respect to Multiple Variables.The Complete Guide to Using the Chain Rule in Calculus for Multiple Composed Functions
Learn how to find relative maxima and minima on a graph with step-by-step instructions and examples