Textbook pdf's

INVESTIGATION
EXAMPLE 1
Use the algorithm for curve sketching to sketch the graph of each of the
following functions. After completing your sketch, use graphing technology to
verify your results.
a. y x 4 3x 2 2x
b. y
x
x 2 1
Sketching an accurate graph of a polynomial function
Use the algorithm for curve sketching to sketch the graph of
f 1x2 3x 3 2x 2 5x.
Solution
This is a polynomial function, so there are no discontinuities and no asymptotes.
The domain is 5xR6. Analyze f (x). Determine any intercepts.
x-intercept, y 0
3x 3 2x 2 5x 0
x13x 2 2x 52 0
x13x 521x 12 0
x 0, x 5 3 , x 1
y-intercept, x 0
y 0
10, 02
10, 02,
a 5 11, 02
3 , 0 b ,
Now determine the critical points.
Analyze f ¿(x).
f ¿1x2 9x 2 4x 5
Setting f ¿1x2 0, we obtain
9x 2 4x 5 0
19x 2 4x 52 0
19x 521x 12 0
x 5 or x 1
9
When we sketch the function, we can use approximate values x 0.6 and
y 1.6 for x 5 and f Q 5 9 9 R.
Analyze f–(x) .
f –1x2 18x 4
At x 5 , At x 1,
9
f – a 5 9 b 18 a 5 9 b 4
10 4
14
6 0
f –112 18112 4
18 4
14
7 0
208 4.5 AN ALGORITHM FOR CURVE SKETCHING
NEL