2. To find the minimum or maximum of a function that is not constrained,
that is, there are no restrictions on range of the function, you take
the derivative of the function, set it equal to zero, and solve for the
variable. The intuition is that the derivative is the instantaneous
slope of the function. A minimum or maximum occurs when the
instantaneous slope equals 0.
a) Using Excel, find the minimum, x*, of f(x) = x2 + 2. What is f(x*)?
Calculate f(x) for x = -2 to 2 at 0.1 intervals. Plot f(x).
b) Calculate the derivative of f(x), f’(x). Set it equal to zero and
solve for x.
Business Homework Solutions
#2843
Minimum and maximum of a function that is not constrained
To find the minimum or maximum of a function that is not constrained, that is, there are no restrictions on range of the function, you take the derivative of the function, set it equal to zero, and solve for the variable. The intuition is that the derivative is the instantaneous slope of the function. A minimum or maximum occurs when the instantaneous slope equals 0.
a) Using Excel, find the minimum, x*, of f(x) = x2 + 2. What is f(x*)? Calculate f(x) for x = -2 to 2 at 0.1 intervals. Plot f(x).
b) Calculate the derivative of f(x), f'(x). Set it equal to zero and solve for x.
The solution clearly explains how to solve for the minimum and maximum plus the derivative of f(x). The commands in Excel at included, as well as a graph is easier understanding.
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