Finding the equation of a tangent at a curve I have a curve $C$ with equation $y=\frac{12}{x^2}+7x-6$ and I was trying to find the equation of the tangent to $C$ at $P$. When point $P$ has $x$ coordinate $2$.
I have thought about getting the y-coordinate from the equation but then I don't know how to get the rest of the things I need for the equation of a straight line?
Apologies if this is Abit basic I have only just learnt about differentiation! Any advice would help!
 A: So first you can get the $y$ coordinate by subbing in $x=2$ into the first equation which I assume you did to get $y=11$. 
For an equation of a straight line we have: $y-y_1=m(x-x_1)$, we have the set of coords above so we can sub that in! This becomes $y-11=m(x-2)$, then as you know $m$ is the gradient. To get this we can differentiate the equation then sub in our x coordinate before to get a value for $m$, I will let you do this though!
A: When you differentiate a equation of a curve you are basically finding it's slope at that particular point.
To find the equation of a tangent you need to find the equation of the line corresponding to the slope you are going to find.
So all you have to do here is that you need to differentiate Curve equation with respect to 'x'
What you find as (dy/dx) is the slope 'm' of the curve at any point.
So after finding dy/dx, keep value of x as provided and you will have the slope of line at the particular point.
Then go back to original equation. Find out the value of y by putting value of x.
After this you have to apply the equation if a straight line which is given by
(y - y1)=m(x - x1)
You have y1 and x1 you have m, this is your required equation.
