When Does Extrema Exist?
From the Two Theorems, the Extrema of a Closed Interval Can Only Occur at Either a Critical Point or an End Point. So to Find the Extrema, Set the Derivative...
From the two theorems, the extrema of a closed interval can only occur at either a critical point or an end point. So to find the extrema, set the derivative equal to 0, and solve.
Where does the extrema occur?
All local maximums and minimums on a function's graph — called local extrema — occur at critical points of the function (where the derivative is zero or undefined).
How do you know if a function is extrema?
Finding Absolute Extrema of f(x) on [a,b]
- Verify that the function is continuous on the interval [a,b] .
- Find all critical points of f(x) that are in the interval [a,b] . ...
- Evaluate the function at the critical points found in step 1 and the end points.
- Identify the absolute extrema.
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