Please help with this problem. I spent 2 hours working in this problem. Nobody in my class got it, so if you get it, you are the smartest person I know.

if f(x) = 3/(6pi - 9x)
Then the slope of the tangent line to the graph of y=f(x) at the point (pi,-3/3pi) is the limit as x tends to ______ of the following expression ___________.

The Value of the limit is _________

It follows that the equation of the tangent line is
y = _____________.

Please help if you can thank you.

Question

Please help with this problem. I spent 2 hours working in this problem. Nobody in my class got it, so if you get it, you are the smartest person I know. 

if f(x) = 3/(6pi - 9x) 
Then the slope of the tangent line to the graph of y=f(x) at the point (pi,-3/3pi) is the limit as x tends to ______ of the following expression ___________.

The Value of the limit is _________

It follows that the equation of the tangent line is 
y = _____________.

Please help if you can thank you.

dumbcow · Answer

slope of tangent line is the derivative of the function at the given point ---> f'(pi)

use chain rule, Let u = 6pi - 9x , du = -9
$$f'(x) = \frac{3}{u} *du = -\frac{3}{u^2}*du = \frac{27}{(6\pi -9x)^2}$$
pluggin in x=pi
$$f'(\pi) = \frac{27}{(-3\pi)^2} = \frac{3}{\pi^2}$$

anonymous · Answer

$$f'(x) = \lim_{x \rightarrow a}\frac{ f(x)-f(a) }{ x-a }$$ ... you want to find the value of this limit (as x tends to the x-coordinate of the given point (a, f(a)) and the expression is what you get when you fill in your given function for f(x) and your given x-coordinate for a and given y-coordinate for f(a).  to then find the equation of the tangent line, you want to use the value of the limit as x approaches a  (that gives you the slope of the tangent line) and the point given with y=mx+b to get the value of b... then you've go tthe equation of the tangent line