Find the slope of the secant line

Question

The point P(9,7) lies on the curve y=√(x)+4

Let Q be the point (x, (√(x)+4)).

 

A) Find the slope of the secant line PQ for the following values of x. (Answers should be correct to at least 6 places after the decimal point)

if x=9.1, the slope of PQ is:

if x=9.01, the slope of PQ is:

if x=8.9, the slope of PQ is:

if x=8.99, the slope of PQ is:

 

B) Based on the above results, estimate the slope of the tangent line to the curve at P(9,7)

 

Answer 1

All you have to do is plug in those values of x to the point (x, (√(x)+4)) to find point Q.

 

In that, x is the x value of the point and we will call it x2.

(√(x)+4) is the y value and we will call it y2.

 

Point P is the starting point, and 9 will be x1 and 7 will be y1.

 

After plugging in the x values to find the different point Qs, you will take (y2-y1)/(x2-x1) for each pair of points to find the slopes of the secant lines. Then estimate the slope of the tangent line, which will be between the slopes for x=8.99 and x=9.01.