Question

Let $f$ be a continuous function on the closed interval $[-1, 4]$, where $f(-1) = 4$ and $f(4) = 1$. Which of the following is guaranteed by the Intermediate Value Theorem? $f(c) = -3$ for at least one $c$ between 1 and 4 $f(c) = -3$ for at least one $c$ between $-1$ and 4 $f(c) = 3$ for at least one $c$ between $-1$ and 4 $f(c) = 3$ for at least one $c$ between 1 and 4

          Let $f$ be a continuous function on the closed interval $[-1, 4]$,
where $f(-1) = 4$ and $f(4) = 1$.
Which of the following is guaranteed by the Intermediate Value
Theorem?
$f(c) = -3$ for at least one $c$ between 1 and 4
$f(c) = -3$ for at least one $c$ between $-1$ and 4
$f(c) = 3$ for at least one $c$ between $-1$ and 4
$f(c) = 3$ for at least one $c$ between 1 and 4

Let f be a continuous function on the closed interval [-1, 4],
where f(-1) = 4 and f(4) = 1.
Which of the following is guaranteed by the Intermediate Value
Theorem?
f(c) = -3 for at least one c between 1 and 4
f(c) = -3 for at least one c between -1 and 4
f(c) = 3 for at least one c between -1 and 4
f(c) = 3 for at least one c between 1 and 4

Added by Sue K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/31/2023

Step 1

In this case, we are given that f is continuous on the closed interval [-1, 4], and f(-1) = 4 and f(4) = 1. We want to find out if f(c) = 3 for at least one number c between 1 and 4. Since f(-1) = 4 and f(4) = 1, we know that f(-1) > 3 and f(4) < 3. Show more…

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Let f be a continuous function on the closed interval [-1,4], where f(-1) = 4 and f(4) = 1. Which of the following is guaranteed by the Intermediate Value Theorem? f(c) = -3 for at least one c between 1 and 4 f(c) = -3 for at least one c between -1 and 4 f(c) = 3 for at least one c between -1 and 4 f(c) = 3 for at least one c between 1 and 4