# Question: the point p5 1 lies on the curve ysquare root...

###### Question details

The point *P*(5, 1) lies on the curve y=square root of
x-4

(a) If *Q* is the point(* x*, square root
of x-4

use your calculator to find the slope of the secant line
*PQ* (correct to six decimal places) for the following
values of *x*.

(i) 4.5

(ii) 4.9

(iii) 4.99

(iv) 4.999

(v) 5.5

(vi) 5.1

(vii) 5.01

(viii) 5.001

(b) Using the results of part (a), guess the value of the slope of
the tangent line to the curve at

* P*(5, 1).

(c) Using the slope from part (b), find an equation of the tangent
line to the curve at

* P*(5, 1).

* y* =

(d) Sketch the curve, two of the secant lines, and the tangent
line.