Question

If $f(x)$ is differentiable on $(a, b)$, which of the following must be true? I. $f(x)$ is continuous on $(a, b)$ II. $f(x)$ is defined for all $x$ in $[a, b]$ III. There exists a point $c$ in $[a, b]$ such that $f(c) = 0$ a. I b. II c. III d. All of these are true.

          If $f(x)$ is differentiable on $(a, b)$, which of the following must be true?
I. $f(x)$ is continuous on $(a, b)$
II. $f(x)$ is defined for all $x$ in $[a, b]$
III. There exists a point $c$ in $[a, b]$ such that $f(c) = 0$
a. I
b. II
c. III
d. All of these are true.

If f(x) is differentiable on (a, b), which of the following must be true?
I. f(x) is continuous on (a, b)
II. f(x) is defined for all x in [a, b]
III. There exists a point c in [a, b] such that f(c) = 0
a. I
b. II
c. III
d. All of these are true.

Added by Danielle G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ben Blakesley

03/29/2022

Step 1

Step 1: If a function is differentiable on an open interval (a, b), then it is also continuous on that interval. Show more…

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If f(x) is differentiable on (a, b), which of the following must be true? I. f(x) is continuous on (a, b) II. f(x) is defined for all x in [a, b] III. There exists a point c in [a, b] such that f(c) = 0 a. I b. II c. III d. All of these are true.