HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010

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For the function
fx
2
+ + 6 …()= x
3
− 4x x
(i) find the intercepts.
(ii) find the turning points.
(iii) draw a sketch graph showing this information.
(iv) find the area under the curve between the two turning points.
Step 1. Enter the function into the
SYMB view of the Function aplet, so
it is available for plotting.
Step 2. Use the
POLYROOT function to find the roots. This function is
in the
MATH menu in the Polynom. group. See page 204 for
more information.
−
The results show that the x intercepts are
(1,0),(2,0)and
(3,0). The y intercept is found by evaluating F1(0) in the
HOME view giving the point (0,6).
Step 3. Switching to the
PLOT view via VIEWS - Decimal, you will
find that the function does not display as well as it could.
Since it is the y axis that is not displaying enough, we will use
the ‘
Y-Zoom Out’ option in the menu after first setting
the
Zoom factors to 2 rather than 4 (which is too drastic).
The
Zoom factors setting is also found in the menu.
pop-up menu to find the Extremum (both
left and right). The snapshot right shows the left-hand turning
point of (0.131,6.065).
Now use the
300