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

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Answer 1 · 2018-03-01T12:26:40

See below.

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

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

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

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

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

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