Calculus
Forgetting to Check Endpoints for Absolute Extrema
Students find only the critical points and forget to test the endpoints when looking for absolute maxima and minima.
Quick check
Why students make it
They mix up local extrema with absolute extrema. The derivative test only finds possible extrema inside the interval, so it can miss the largest or smallest value at an endpoint.
The rule done right
For a continuous function on a closed interval , absolute extrema can occur at critical points or at endpoints. Find all critical points in , evaluate the function there and at and , then compare the values.
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Critical Points and Extrema Infographic -
Calculus, The Extreme Value Theorem Infographic -
Calculus, Absolute vs Local Extrema Infographic -
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