The point P(3,1) lies on the curve y= (3/x). if Q is the point (x, (3/x), find the slope of the secant line PQ for the following values of x.

Question

if x=3.1, the slope of PQ is:

if x= 3.01, the slope of PQ is:

if x= 2.9, the slope of PQ is:

is x=2.99, the slope of PQ is:

based on the above results, guess the slope of the tangent line to the curve at P(3,1).

Answer 1

I will not do this for you...you need to do it all by yourself to understand what is being asked.

I will, however, start you off.

If x = 3.1, y = 1/3.1 and you should do this division on your calculator.

Then compute the slope of the straight line between the point you just calculated and (3,1).

The repeat for the other values and look at the result. Then answer the question!