- #1
silverbomb20
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Homework Statement
FIND THE ABSOLUTE MINIMUM AND ABSOLUTE MAXIMUM OF:
f(x) = 9x + 1/x
on the interval [1,3]
Homework Equations
The Attempt at a Solution
I don't know how to get started!
No. Try again.silverbomb20 said:okay so that's going to give me 9x^2=x^2?
silverbomb20 said:or does that -1x^-2 not cancel?
The absolute minimum and maximum refer to the lowest and highest values that a function can reach over a given interval. This means that there are no other values in the interval that are smaller or larger than the absolute minimum and maximum, respectively.
To find the absolute minimum and maximum of a function, you need to take the derivative of the function, set it equal to zero, and solve for the critical points. Then, plug these critical points into the original function to determine which one is the absolute minimum and which one is the absolute maximum.
The relative minimum and maximum refer to the lowest and highest points of a function within a specific interval, while the absolute minimum and maximum refer to the lowest and highest points of a function over the entire domain.
No, a function can only have one absolute minimum and one absolute maximum. This is because these values are the lowest and highest points that a function can reach over its entire domain.
Absolute minimum and maximum are commonly used in optimization problems, where the goal is to find the most efficient or cost-effective solution. These values can also be used in economics to determine the maximum profit or optimal production level for a company.