# `f(x) = sqrt(x), [1,9]` Use a graphing utility to (a) graph the function `f` on the given interval, (b) find and graph the secant line through points on the graph of `f` at the endpoints of...

`f(x) = sqrt(x), [1,9]` Use a graphing utility to (a) graph the function `f` on the given interval, (b) find and graph the secant line through points on the graph of `f` at the endpoints of the given interval, and (c) find and graph any tangent lines to the graph of `f` that are parallel to the secant line.

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### 1 Answer

a) the graph is here: https://www.desmos.com/calculator/kdzzqcpt3q

b) the endpoints of the graph are (0, 0) and (9, 3). The slope of the secant line is 1/3, the equation is y=x/3.

c) f'(x)=1/(2*√x), it is =1/3 only at x0=9/4=2.25.

f(x0)=3/2=1.5.

So the equation of the tangent line is

y=(1/3)*(x-9/4)+3/2.