Refer to the graph on p. 221. The function is given by f ( x ) = x 2 − 1 x 2 + x − 6 . a. Inspect the graph and estimate the coordinates of any extrema. b. Find f ' and use it to determine the critical values. ( Hint: you will need the quadratic formula .) Round the x -values to the nearest hundredth. c. Graph f in the window [ 0 , 0.2 , 0.16 , 0.17 ] . Use trace or maximum to confirm your results from part (b). d. Graph f in the window [ 9.8 , 10 , 0.9519 , 0.95195 ] . Use trace or minimum to confirm your results from part (b). e. How close were your estimates of part (a)? Would you have been able to identify the relative minimum point without calculus?
Refer to the graph on p. 221. The function is given by f ( x ) = x 2 − 1 x 2 + x − 6 . a. Inspect the graph and estimate the coordinates of any extrema. b. Find f ' and use it to determine the critical values. ( Hint: you will need the quadratic formula .) Round the x -values to the nearest hundredth. c. Graph f in the window [ 0 , 0.2 , 0.16 , 0.17 ] . Use trace or maximum to confirm your results from part (b). d. Graph f in the window [ 9.8 , 10 , 0.9519 , 0.95195 ] . Use trace or minimum to confirm your results from part (b). e. How close were your estimates of part (a)? Would you have been able to identify the relative minimum point without calculus?
Solution Summary: The author explains how the graph on page 221 shows the relative maxima at the point (0,16).
Refer to the graph on p. 221. The function is given by
f
(
x
)
=
x
2
−
1
x
2
+
x
−
6
.
a. Inspect the graph and estimate the coordinates of any extrema.
b. Find
f
'
and use it to determine the critical values. (Hint: you will need the quadratic formula.) Round the x-values to the nearest hundredth.
c. Graph
f
in the window
[
0
,
0.2
,
0.16
,
0.17
]
. Use trace or maximum to confirm your results from part (b).
d. Graph f in the window
[
9.8
,
10
,
0.9519
,
0.95195
]
. Use trace or minimum to confirm your results from part (b).
e. How close were your estimates of part (a)? Would you have been able to identify the relative minimum point without calculus?
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Suppose a certain drug is administered to a patient, with the percent of a concentration of the drug in the bloodstream t hours later given by
K(t)=5t/t^2+1
On what interval is the concentration of the drug increasing?
On what interval is the concentration decreasing?
When is the concentration reaching extremum? Is it a minimum or maximum?
Precalculus Enhanced with Graphing Utilities (7th Edition)
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