Thread: Calculus/tangent line

Find all values of x at which the tangent line to the given curve passes through the origin for y = 1/(x + 4)

Originally Posted by pantera

Find all values of x at which the tangent line to the given curve passes through the origin for y = 1/(x + 4)

The tangent is a line of slope "m".

The derivative of the function gives this slope.

As the tangent passes through the origin, it's equation is y=mx, as c=0.

Hence, the point of intersection of this tangent and the curve gives us x.



The equation of the tangent(s) through (0,0) is

Solving f(x) for the curve = mx for the line finds x.



Solving this, bearing in mind that x=-4 is not part of the domain of f(x) or f'(x) discovers x.

Hence multiply both fractions by (x+4) before solving for x.

Lines look like this:

We know we need the Origin:

The derivative gives the slope:

We know:

I'm a little surprised to find only one solution. I expected two solutions when I started the problem. I was wrong.

Let's see what you get.

Here's why there is only one solution