• Oct 22nd 2005, 11:55 PM
mathhelp
Hello, I have been working on this question for a couple of days now, have no idea about it, please help...

A polynomial function is defined by f(x) = x^3 + 2x^2 - 5x - 6

a) Deteremine the coordiantes of four points on the graph of f(x). choose the points so the tangent line at each point is a side of a parallelogram.

b) Determine the equations of the four tangents lines in part a.

c) sketch a graph of f(x) and the tangent lines. also clearly mark the parallelogram on this graph.

Pleas help... thanx in advance
• Oct 24th 2005, 04:44 PM
hpe
Quote:

Originally Posted by mathhelp
Hello, I have been working on this question for a couple of days now, have no idea about it, please help...

A polynomial function is defined by f(x) = x^3 + 2x^2 - 5x - 6

a) Deteremine the coordiantes of four points on the graph of f(x). choose the points so the tangent line at each point is a side of a parallelogram.

b) Determine the equations of the four tangents lines in part a.

c) sketch a graph of f(x) and the tangent lines. also clearly mark the parallelogram on this graph.
x^3

Pleas help... thanx in advance

You are essentially free to choose the slopes of the parallelogram sides as you wish. For example, choose a parallelogram with sides parallel to the x-axis (slope = 0) and with slopes equal to 1. Then you have to find the solutions of f '(x) = 0 (2 solutions) and f '(x) = 1 (two more solutions). These are your four points. The tangent lines at these four points are found as usual. If the four points turn out to be weird numbers, solve, e.g. f '(x) = 2 or f '(x) = -1 until you get nice solutions.