fixed the problem becaise i submitted it wrongf beforehand

Question

The point P(1/2,10) lies on the curve y=5x.

If  is the point (x,5/x), find the slope of the secant line PQ for the values below of .If x=0.6, the slope of PQ is:   and if x=0.51, the slope of PQ is:   and if x=0.4, the slope of PQ is:   and if x=0.49, the slope of PQ is:   

Based on the results, guess the slope of the tangent line to the curve at P(0.5,10).

Answer 1

I believe that the function is y = 5/x.

The points (1/2, 10) and (x, 5/x) lie on the graph of this function.

Slope of secant line joining (x, 5/x) and (1/2, 10) is (5/x - 10) / (x - 1/2)

Plug in the given x values to find the slopes of the various secants.

Note: as x gets closer and closer to 1/2, the secant line slopes should get closer and closer to -20,which is the slope of the tangent line to the curve y = 5/x at the point (1/2, 10).