AP Calculus AB 1.16: Intermediate Value Theorem

Practice AP Calculus questions on applying the Intermediate Value Theorem to continuous functions on closed intervals and justify existence claims.

[Maximum number: 2]

A student starts reading a book at time t=0 minutes and continues reading for the next 10

minutes. The rate at which the student reads is modeled by the differentiable function R, where

R(t) is measured in words per minute. Selected values of R(t) are given in the table shown.

Must there be a value c, for 0<c<10, such that R(c)=155 ? Justify your answer.

R is differentiable implies R is continuous.	Differentiable implies continuous	Point 3 (P3)
R(0)=90<155<R(10)=162	Answer with justification	Point 4 (P4)
Therefore, by the Intermediate Value Theorem, there must be a value c, with 0<c<10, such that R(c)=155.

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FUN-1.A—Explain the behavior of a function on an interval using the Intermediate Value Theorem question 1