the point P(7,1) lies on the curve y equals the square root of x - 6.?

Question

If Q is the point (x, square root of x -6), use your calculator to find the slope of the secant line (correct to six decimal places) for the following values of

Answer 1

slope of secant line is
(y-1)/(x-7)
[sqr(x-6)-1]/( x-7)
what is the number want to find though
the exact answer is 1/2
estimate is .513167

Answer 2

The first derivative: y' = -x/y which can be written as y' = -x.y^(-1) Differentiate again using product rule: y'' = (x/y²) y' - (1/y) y'' = (x/y²) (-x/y) - (1/y) y'' = -(x² + y²) / y³ Sub in (0, √10) then y'' = -(0 + 10) / (√10)³ = -1/√10