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
After a great deal of experimentation, two college senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked,
its cork travels according to the function below, where s is its height (in feet) above the ground t seconds after being released.
s(t)=-16t² + 30t+3
a. How high will it go?
b. How long is it in the air?
+6x²+135x+1) (0≤x≤10). a) Find the number of units
The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In (-x²+6x² + 135x+
that should be sold in order to maximize the total profit. b) What is the maximum profit?
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the
population in the year 2000 was 22600.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
Chapter 2 Solutions
Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
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