Question

The point P (3,1) lies on the curve y=sqrt(x-2).

a. If Q is the point (x, sqrt(x-2), use the difference quotient formula to find the slope of the secant line PQ (correct to four decimal places) for the following values of x:

i. 2.5=
ii. 2.9=
iii. 2.99=
iv. 2.999=
v. 3.5=
vi. 3.1=
vii. 3.01=
viii. 3.001=

b. Using the results of part (a), guess the value of the slope of the tangent line to the curve at the point P(3,1).

c. Using the slope from part (b), find an equation of the tangent line to the curve at the point P(3,1).