Modeling with Rational and Piecewise-Defined Functions: Part Two — Test

Question 8 • Precalculus

Over the closed interval left bracket 3 comma 8 right bracket , for which function can the extreme value theorem be applied?

Answer

h of x is equal to the fraction with numerator open paren x minus 5 close paren times open paren x minus 1 close paren and denominator x squared minus 25

h of x equals inequality negative x comma x is less than 5 inequality x squared minus 20 comma x is greater than or equal to 5

h of x equals inequality the fraction with numerator 9 x and denominator 10 minus x comma x is less than 4 inequality x plus 2 comma x is greater than or equal to 4

h of x is equal to the fraction with numerator negative 2 and denominator 5 times open paren x minus 4 close paren squared

Explanation

The extreme value theorem applies to a function that is continuous on the entire closed interval [3, 8]. In choice C, the two formulas meet at x = 4: the left-hand formula gives 9(4)/(10 − 4) = 6, and the right-hand formula gives 4 + 2 = 6. Both formulas are continuous on their parts of the interval, so choice C is continuous throughout [3, 8]. The other choices have a discontinuity or are undefined at a point in the interval.

AI-written and checked against the verified answer.

More from this Course

Test

Test

Test