7. [-/14.32 Points] DETAILS
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SCALCET8 2.5.055.
PRACTICE ANOTHER
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.
$e^x = 4 - 3x$, $(0, 1)$
The equation $e^x = 4 - 3x$ is equivalent to the equation $f(x) = e^x - 4 + 3x = 0$. $f(x)$ is continuous on the interval $[0, 1]$, $f(0) =
$
f(1) =
. Since ---Select--- < 0 < ---Select---, 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 $e^x = 4 - 3x$, in the interval $(0, 1)$.
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