Question

How do you find the slope of the secant lines of `f(x) = sqrtx` at x=1?

Answer 1

See below.

Explanation:

A secant line to the graph of `f(x) = sqrtx` through the points where `x=1` and `x=1+h`, has slope

`(f(1+h)-f(1))/h = (sqrt(1+h)-1)/h`

`= ((sqrt(1+h)-1))/h * ((sqrt(1+h)+1))/((sqrt(1+h)+1))`

`=( (1+h)-1)/(h(sqrt(1+h)+1))`

`= 1/(sqrt(1+h)+1)`