Say we have some positive value K. How can we know what K is if the function $f(x)=K tan(x)$ intersects its derivative perpendicularly on a graph?
So I know how to do this using some form of a software but don't know how to do it theoretically, or by paper and pencil, to make sure I am getting the same value. How I tried to approach the problem: $f(x)=K tan(x)$. $f(x)'=K sec^2(x)$. Then we have $-K/sec^2(x)$ since we are trying to find the derivative perpendicularly. Then to find K, I set the the two equal and that is where I am stuck. Any help with shown steps would be appreciated.