Question

Could someone explain me in a very simple way.
How to find the equation of a line tangent to something.

Answer 1

To find the slope of the line that is tangent to a function, take the first derivative of the function. If you find the first derivative to be, say, 2x, use a point on your graph and fill in the x value from it and that value you get is the slope. Now go back to that point you used, the (x,y) point that is on your line, and use it and the slope you found at that point to rewrite the equation in point slope form. I will try to give you an example. Ok?

Answer 2

The first derivative of that function is y' = 2x, right? Point (1,1) is on the graph. So plug in the x coordinate of that point, the 1, into the x value in your derivative and get
y' = 2(1) = 2. That is the slope of that line at that exact point. Now take your point, (1,1) and use it in the point-slope equation to write the equation using the slope of 2. It would be y-1 = 2(x-1) y-1 = 2x - 2 y = 2x - 1. And that is the equation of the line that is tangent to your graph at point (1,1). You could do it with any given (known) point on any graph.

Answer 3

Hope this helps!

Answer 4

@IMStuck Thank you