Question

20. By the mean-value theorem, if $f(x)$ is continuous on the interval $[a, b]$, then at some point on that interval $f'(x)$ is equal to A) frac{b-a}{f(b)-f(a)} B) frac{f(b)-f(a)}{b-a} C) $f(b)-f(c)$ D) 0 E) None of the above 21. If $f(x)$ is continuous on the interval $[0,3]$ and $f(0) = -3, f(3) = 5$ then which of the following must be true? I. $f(x)$ has a root on the interval. II. $f(x)$ has a local maxima or minima on the interval. III. $f'(x)$ is equal to 8/3 at some point on the interval. A) I only B) II only C) III only D) I and III E) I and II

          20. By the mean-value theorem, if $f(x)$ is continuous on the interval $[a, b]$, then at some point on
that interval $f'(x)$ is equal to
A) frac{b-a}{f(b)-f(a)}
B) frac{f(b)-f(a)}{b-a}
C) $f(b)-f(c)$
D) 0
E) None of the above
21. If $f(x)$ is continuous on the interval $[0,3]$ and $f(0) = -3, f(3) = 5$ then which of the following
must be true?
I. $f(x)$ has a root on the interval.
II. $f(x)$ has a local maxima or minima on the
interval.
III. $f'(x)$ is equal to 8/3 at some point on the
interval.
A) I only
B) II only
C) III only
D) I and III
E) I and II

$20. By the mean-value theorem, if f(x) is continuous on the interval [a, b], then at some point on that interval f'(x) is equal to A) fracb-af(b)-f(a) B) fracf(b)-f(a)b-a C) f(b)-f(c) D) 0 E) None of the above 21. If f(x) is continuous on the interval [0,3] and f(0) = -3, f(3) = 5 then which of the following must be true? I. f(x) has a root on the interval. II. f(x) has a local maxima or minima on the interval. III. f'(x) is equal to 8/3 at some point on the interval. A) I only B) II only C) III only D) I and III E) I and II$

Added by Paula R.

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