AP Calculus BC 1.16 Working with the Intermediate Value Theorem Ivt Questions

Practice AP Calculus BC questions on checking continuity and endpoint values before applying the Intermediate Value Theorem.

Covered syllabus points

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

[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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Covered syllabus points

Question 1