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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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