Limits and Continuity — Quiz

Question 1 • Precalculus

For which function and interval can the extreme value theorem be applied?

Answer

f of x is equal to the fraction with numerator x and denominator open paren x minus 6 close paren squared over the interval left bracket 3 comma 5 right bracket

f of x is equal to 4 tangent pi x over the interval left bracket 0 comma 1 right bracket

f of x is equal to the fraction with numerator negative 5 and denominator 2 times open paren x minus 7 close paren cubed over the interval open paren 6 comma 8 close paren

f of x is equal to 3 e to the x th power plus 1 over the interval open paren 1 comma 3 close paren

Explanation

The extreme value theorem applies when a function is continuous on a closed, bounded interval. In choice A, f(x) = x/(x − 6)² is continuous throughout [3, 5], since its denominator is never zero there, and the interval is closed and bounded. The other choices either include a discontinuity or use an open interval.

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