The point P ( 1/ 4 , 16 ) lies on the curve y = 4/ x . If Q is the point ( x , 4/ x ) find the slope of the secant line P Q for the following values of x .

Question

If x=0.35, the slope of PQ is

and if x=0.26, the slope of PQ is

if x=0.15, the slope of PQ is

if x=0.24, the slope of PQ is

Based on the above results, guess the slope of the tangent line to the curve at P(0.25,16)

Answer 1

The slope of secant line combaining point P(1/4, 16) and point (x, 4/x) m = (4/x - 16)/(x - 1/4);

x = 0.35; m = - 45.71.43.

x = 0.26; m = - 61.5385.

x = 0.15; m = - 106.6667

x = 0.24; m = - 66.6667

I still can't make conclusion.

Let take closer to 0.25:

x = 0.251 m = - 63.7450

x = 0.249 m = - 64.2570

So slope of tangent line at point P(1/4, 16) m = - 64