Homework 11/8
This worksheet is about locating the root of the function
f
(
x
) = 0
.
5
x
3

x

0
.
5
e

x
, which is
graphed below. You will end up with a lot of messy decimals as you work these problems. Keep
every decimal accurate to at least 5 places.
–2
–1
1
2
–2
–1
1
2
1. Assume that
x
= 1 is the root. (This is wrong, but that’s ok.)
(a) Find
f
(1). (If you get zero, then 1
is
the root and you can quit.)
(b) Find the equation of the tangent line at
x
= 1.
(c) Graph the tangent line on the graph of
f
provided above.
(d) Find where the tangent line crosses the
x
axis.
1
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2. If your last answer was not
x
= 2, then go back and find your mistakes.
If it was
x
= 2,
assume that
x
= 2 is the root. (This is wrong, but that’s ok.)
(a) Find
f
(2). (If you get zero, then 2
is
the root and you can quit.)
(b) Find the equation of the tangent line at
x
= 2.
(c) Graph the tangent line on the graph of
f
provided above.
(d) Find where the tangent line crosses the
x
axis.
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 Fall '08
 STAFF
 Calculus, Decimals, Decimal

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