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Ilia_Sergeevich [38]
3 years ago
14

If the interval (a, infinity) describes all values of x for which the graph of f(x)=4/x^2-6x+9 is decreasing, what is the value

of a
Mathematics
2 answers:
Afina-wow [57]3 years ago
7 0

Answer:

The answer is "3".

Step-by-step explanation:

\texttt{Given graph equation: } \\\\\bold{\Rightarrow f(x)=\frac{4}{x^2-6x+9} }

\bold{\ interval:  (a,\infty)}

differentiate the function f(x):

\Rightarrow f'(x) = \frac{d }{dx}(\frac{4}{x^2-6x+9})\\\\

Formula:

\bold{\frac{d}{dx} \frac{v}{u}= \frac{u \frac{d}{dx} v- v\frac{d}{dx}u }{u^2}}

\Rightarrow f'(x) = \frac{d }{dx}(\frac{4}{x^2-6x+9})\\\\\\\Rightarrow f'(x) = \frac{d }{dx}(\frac{(x^2-6x+9) \frac{d}{dx} 4- 4\frac{d}{dx}(x^2-6x+9) }{(x^2-6x+9)^2})\\\\\\\Rightarrow f'(x) = \frac{d }{dx}(\frac{(x^2-6x+9) \times 0 - 4(2x-6) }{(x^2-6x+9)^2})\\\\\\\Rightarrow f'(x) =  \frac{- 4(2x-6)}{(x^2-6x+9)^2}\\\\\\\Rightarrow  \frac{- 4(2x-6)}{(x^2-6x+9)^2}=0\\\\\Rightarrow - 4(2x-6)=0\\\\\Rightarrow  8x-24=0\\\\\Rightarrow  8x=24\\\\\Rightarrow  x=\frac{24}{8}\\\\\Rightarrow  x=3\\\\

since the value of x in: (-3 ,\infty) \ \  and  \ \ (3, \infty) and f'(x). So, the value of a is 3

wariber [46]3 years ago
6 0

Answer:

3

Step-by-step explanation:

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3,425,645 rounded to the nearest hundred thousand
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Answer:

3,400,000

Step-by-step explanation:

refer to attached for reference

in our case, the digit in the hundred thousands place is the number 4.

How we round this digit depends on the digit directly to the right of it (i.e the ten-thousands place).

If the digit to the right is less than 5, then leave the digit in the hundred thousands place the same and make everything else to the right zeros.

if the digit to the right is 5 or greater, then increase the digit in the hundred thousands place by 1 and then make everything else to the right zeros.

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Answer:

9

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3 years ago
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