Question

The point P(4,2) lies on the curve y=x^1/2

If Q is the point (x,x^1/2) use your calculator to find the slope of the secant line PQ for the following values of X:
1)3.5
2)3.9
3)3.99
4)3.999
5)4.5
6)4.1
7)4.01
8)4.001

i plugged these points into the intial equation and got that it was approaching 2. and i made it the slope of secant. however, my friend got a different answer; she found the slope using delta y over delta x. who is right and why?

thanks for any help!

Answer 1

4) If the coordinates of Q are
x = 3.999, y = 1.99975
then the slope of the "secant" line between Q and P (4,2) is
(.00025)/.001 = 0.2500 = 1/4

The exact value of the slope of the tangent to the y(x) curve at P is dy/dx = (1/2)/sqrt x = 1/4

For points Q farther from P, you will get a slightly different answer