Determine the equation of the tangent line

[Blablablabla]

Homework Statement

\frac{3x+6}{2-x}

at x=3

Homework Equations

y - y_{o} = m(x-x_{o})

The Attempt at a Solution

f(3) = -\frac{15}{4}

m = \frac{3}{0} DNE



I have to write the equation in the form of the point-slope formula.

I can get x_{o} and y_{o}, but I am having trouble finding m.

Thanks for any help.

 

[LCKurtz]

You didn't give an equation. I suppose it is$$
y=\frac{3x+6}{2-x}$$You need to calculate its derivative at $3$ to get the slope. You might also check your $f(3)$.

 

[Blablablabla]

Sorry, yes that is the equation. Can you help me find the derivative? I'm a bit confused because my textbook says that the derivative is

\frac{f(x+h)-f(x)}{h}

but in class we learned that as the difference quotient, and that the derivative is when you do this:

y = x^{n}
y' = nx^{n-1}

Thanks for the fast reply

 

[LCKurtz]

Sorry, yes that is the equation. Can you help me find the derivative? I'm a bit confused because my textbook says that the derivative is

\frac{f(x+h)-f(x)}{h}

That is not the derivative of f(x). You have to take the limit as $h \to 0$ to get the derivative.

but in class we learned that as the difference quotient, and that the derivative is when you do this:

y = x^{n}
y' = nx^{n-1}

Thanks for the fast reply

That gives the rule for differentiating powers, which is derived from the difference quotient by letting $h\rightarrow 0$. For more complicated derivatives like your quotient, you would use the quotient rule and the power rule. Haven't you had the quotient rule?