To make things easier, first rewrite
<em>f(x)</em> = <em>x</em> / (<em>x</em> + 7/<em>x</em>) = <em>x</em> ² / (<em>x</em> ² + 7)
i.e. multiply <em>f</em> by <em>x</em>/<em>x</em>, which is valid because <em>x</em> can't be 0 anyway as it's outside the domain of <em>f</em>.
Now, by the quotient and chain rules, we get
<em />
<em>f '(x)</em> = ((<em>x</em> ² + 7) (<em>x</em> ²)' - <em>x</em> ² (<em>x</em> ² + 7)') / (<em>x</em> ² + 7)²
… = (2<em>x</em> (<em>x</em> ² + 7) - <em>x</em> ² (2<em>x</em>)) / (<em>x</em> ² + 7)²
… = (2<em>x</em> ³ + 14<em>x</em> - 2<em>x </em>³) / (<em>x</em> ² + 7)²
… = 14<em>x</em> / (<em>x</em> ² + 7)²
<em>f ''(x)</em> = ((<em>x</em> ² + 7)² (14<em>x</em>)' - (14<em>x</em>) ((<em>x</em> ² + 7)²)') / ((<em>x</em> ² + 7)²)²
… = (14 (<em>x</em> ² + 7)² - (14<em>x</em>) (2 (<em>x</em> ² + 7)² (<em>x</em> ² + 7)')) / (<em>x</em> ² + 7)⁴
… = (14 (<em>x</em> ² + 7)² - (14<em>x</em>) (2 (2<em>x</em>) (<em>x</em> ² + 7)²)) / (<em>x</em> ² + 7)⁴
… = (14 (<em>x</em> ² + 7)² - 4<em>x</em> (14<em>x</em>) (<em>x</em> ² + 7)²) / (<em>x</em> ² + 7)⁴
… = 14 (<em>x</em> ² + 7)² (1 - 4<em>x</em>) / (<em>x</em> ² + 7)⁴
… = 14 (1 - 4<em>x</em>) / (<em>x</em> ² + 7)²
… = (14 - 56<em>x</em>) / (<em>x</em> ² + 7)²
The value of constant a is -3.
Curve 
is shown on the line y = 3.
We have to show that the curve can be rearranged as 
where we have to find the constant a.
We have the given curve:-
Adding 1 on both sides of the equation, we get
y + 1 = 
Squaring the equation on both sides, we get,
= x + 4
Subtracting 4 from both the sides of the equation, we get,
x = 
.
x = 
Hence, we have shown the curve in the form of .
Now,
Comparing it with , we get,
a = -3.
To learn more about equation, here:-
brainly.com/question/10413253
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The correct answer is: [B]: " f(x) = 4(9)ˣ" .
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Note:
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Given: "f(x) = 4* (3²)ˣ '
Note that: "(3²) = "(3*3) = 9;
So; "4* (3²)ˣ " = 4*(9)ˣ ;
which is: Answer choice: [B]: " f(x) = 4(9)ˣ " .
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-3x-7+4x+7
Negative -7 and positive 7 will give you 0.
So we're left with x. Therefore, the answer is x.
