Question

PLS HELP!! MEDALS!!
basic calc question

Answer 1

Let a = 3 and find an equation of the line tangent to \[y = \frac{ 27 }{ x ^{2} + 9 }\] at x = 2

Answer 2

I'm not exactly sure why your teacher put in the bit of info `Let a = 3 `. That seems to play no role here.

Answer 3

What I would do is first write \[\Large y = \frac{27}{x^2+9}\] as \[\Large y = 27(x^2+9)^{-1}\]

Answer 4

does that help?

Answer 5

another way is to day that \[\left(\frac{1}{f}\right)'=-\frac{f'}{f^2}\]

Answer 6

so in the formula for the equation of the tangent line, y - f(a) = mtan(x - a), do I put 2 in for a?

Answer 7

take the derivative
replace \(x\) by \(2\) i.e. find \(f'(2)\) that is your slope

Answer 8

and yes, you put 2 for \(a\) in the point slope formula after you find \(m\)

Answer 9

But when I do that I get \[y = \frac{ -108 }{ 169 }(x - 2) + \frac{ 27 }{ 169 }\]

Answer 10

I mean
\[\frac{ 27 }{ 13 }\]