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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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Answer:

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Step-by-step explanation:

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2 years ago
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Varvara68 [4.7K]

Answer:

Scale factor = 4 and it represents an 'enlargement'.

Step-by-step explanation:

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7 0
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If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n
natali 33 [55]

Answer:

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Step-by-step explanation:

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To find inverse of a function , replace f(t) with y

y= 100 \cdot  2^\frac{t}{3}

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x= 100 \cdot  2^\frac{y}{3}

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