If the equation of a curve is . It shows that the curve has a minimum point of (4,-1).
Now, if I have a modulus of this equation, that is , the turning point would be (4,1). Is the turning point a maximum point or minimum point now?
If the equation of a curve is . It shows that the curve has a minimum point of (4,-1).
Now, if I have a modulus of this equation, that is , the turning point would be (4,1). Is the turning point a maximum point or minimum point now?
Suppose x is close to 4, say x= 3.9 or x= 4.1. If x= 3.9 [tex]= |(-.1)^2- 1|= |.01- 1|= |-.99|= .99 which is less than 1. If x= 4.1, which is also less than 1. Now, do YOU think (4,1) is a maximum or minimum point?
There are, in fact, three turning points for that graph, (3, 0), (4, 1), and (5, 0).
Hello, Punch!
Visualize their graphs . . .The equation of a curve is .
It shows that the curve has a minimum point of (4,-1).
Now, if I have a modulus of this equation, that is: ,
. . the turning point would be (4,1).
Is the turning point a maximum point or minimum point now?
The graph of the parabola looks like this:Code:| | * * | | | * * | --+----*-------------*----- | * * | * * | * |
There is an absolute minimum at (4, -1).
There is no maximum.
With absolute values, any point below the -axis
. . is reflected upward.
The graph of the modulus function is:
Code:| | * * | | * | * * * * | * * --+----*-------------*----- | 3 5 |
It has absolute minimums at (3,0) and (5,0).
. . and a relative (local) maximum at (4,1).