AP Calculus BC Fun 1 A Explain the Behavior of a Function on an Interval Using the Intermediate Value Theorem Questions

Practice AP Calculus BC questions on applying the Intermediate Value Theorem to continuous functions and justifying existence claims.

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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.

Table for Question AP Calculus BC Fun 1 A Explain the Behavior of a Function on an Interval Using the Intermediate Value Theorem Questions question 1 — AP Calculus BC

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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AP Calculus BC Fun 1 A Explain the Behavior of a Function on an Interval Using the Intermediate Value Theorem Questions question 1