I know this is a repeat question, but the last post didn't answer all my questions, sorry about this.
The expression : lim [√(h+9) -3]/ h as h --> 0 represents the slope of the tangent of some function f(x) when x = 4.
Determine the function y = f(x).
how would the function look like ?
Would the function just be y = f(4)?
I think the expression must equal the slope of the tangent when x=9.
If f(x) = √x then at x=9 the difference quotient is the expression you gave.
No way it could also be the slope at x=4. That would involve
√(4+h) - √4