how do i find the instant slope of a curved line?

Question

I want to know how to find the slope at any point of a curved line without using secant lines i think that the formula has something to do with 

 

f' 

 

but i have do idea 

Answer 1

To find the slope at a point along a curved line, you find the first derivative of the function and evaluate it at that point.  f' is the notation for the first derivative of the function f.  While finding derivatives is usually a couples chapters of calculus, one way is to lessen the distance between the two endpoints of the secant line until it approaches zero.  You said you don't want to use that - So, other methods involved various "rules" to find derivatives.  If you have a specific function, I can show you how to find the derivative....