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Ede4ka [16]
3 years ago
9

F(x) =

Mathematics
1 answer:
Oksana_A [137]3 years ago
4 0

9514 1404 393

Answer:

  f'(x) = (-6x² -14x -23)/(x² +5x +2)²

  f''(x) = (12x³ +42x² +138x +202)/(x² +5x +2)³

Step-by-step explanation:

The applicable derivative formula is ...

  d(u/v) = (v·du -u·dv)/v²

__

  f'(x) = ((-x² -5x -2)(4x +4) -(2x² +4x -3)(-2x -5))/(-x² -5x -2)²

  f'(x) = (-4x³ -24x²-28x -8 +4x³ +18x² +14x -15)/(x² +5x +2)²

  f'(x) = (-6x² -14x -23)/(x² +5x +2)²

__

Similarly, the second derivative is the derivative of f'(x).

  f''(x) = ((x² +5x +2)²(-12x -14) -(-6x² -14x -23)(2(x² +5x +2)(2x +5)))/(x² +5x +2)⁴

  f''(x) = ((x² +5x +2)(-12x -14) +2(6x² +14x +23)(2x +5))/(x² +5x +2)³

  f''(x) = (12x³ +42x² +138x +202)/(x² +5x +2)³

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Step-by-step explanation:

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Answer:

By rounding up of the constant and coefficient terms, we have;

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Step-by-step explanation:

The table for the data on the number of movie admissions each year is presented as follows;

Year, x                                             {}                      Admission, y

0                                                      {}                         1.24

2                                                       {}                        1.26

4                                                      {}                         1.39

6                                                      {}                         1.47

8                                                      {}                         1.49

10                                                      {}                        1.57

Using a graphing calculator, we have that the line of best fit is given by the following equation;

y = 1.23047619048 + 3.45714285714 × 10⁻²·x

Which is approximately, y = 1.23 + 3.46 × 10⁻²·x

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