Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 9 − 8x, (0, 1)
The equation
ex = 9 − 8x
is equivalent to the equation
f(x) = ex − 9 + 8x = 0.

f(x)
is continuous on the interval
[0, 1],

f(0) =
,
and
f(1) =
.
Since

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< 0 <
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,
there is a number c in
(0, 1)
such that
f(c) = 0
by the Intermediate Value Theorem. Thus, there is a root of the equation
ex = 9 − 8x,
in the interval
(0, 1)