I have my notes from class and there is an example in the book but I am not sure what I am doing. The point P(4,28) lies on the curve Y = x^2+x+8. If Q is the point (x,x^2+x+8), find the slope of the secant line PQ for the following values of x.
If x = 4.01, then the slope of PQ is:
and if x = 4.01, the slope of PQ is:
and if x = 3.9, the slpe of PQ is:
and if x = 3.99, the slope of PQ is:
Based on the above results, guess the slpoe of the tangent line to the curve at P(4,28).
If you could give me a hint so I can finish this one and do the other problems I would appreciate it
Thank you again!!!!!!!!
February 8th 2007, 12:47 PM
The math behind slope is very simple to work with once you understand it. Perhaps you should review notes or your text on that. At the least, you need to remember that slope describes the incline or decline of a line. You only need two points to find it, (X1, Y1) and (X2, Y2). The slope m = (Y2-Y1)/(X2-X1). You can use any two points on the line. The slope of the line tells you how much the line moves up (increase in Y) for a move in the horizontal (increase in X). That is, if m = 2, then for every step to right one unit, the line moves up two units. For every step to the right 100 units, the line moves up 200 units.
Do you understand the function of slope, how to find it given two points, and what it tells us about a line?
The purpose of this exercise is to approximate the tangent slope of a curve. If you draw it out, I think you will understand. Sketch the curve and the secants, and use the slope formula to find the slope of each secant. Then, with these numbers, guess what the tangent slope is.