regardin point of inflexion and turning point (1 Viewer)

[gh0stface]

1. firstly the stationary point has the nature maxima/minima TP or the point of inflexion rite?

2. a stationary point is a point of inflexion when from the first deriviative, using the table of values the signs are both + or both -. rite?

3.the points of inflexion can also be determined by the 2nd deriviative when y'=o and the 2nd condition where the sign change if u sub in a number less/higher than x. ---- But wat if it doesnt change? what happens? and also to test if the sign changes, do u hav to sub in numbers within the region of the turning points or can it be anything lower/higher than x?

4. how would u draw a point of inflexion? how would u noe if its this "\" or "/" using the 1st and 2nd deriviative to work out.


thanks

 

[Foxodi]

1. yes... you have a textbook right?
2. its a potential point of inflexion... then you test it into the 2nd derivative, and then use the table of values.
3. if y' = o and y''=0, then its a horizontal point of inflexion
4. First derivative will show if its \ or /... f'(x)>0 its /, etc etc.

 

[PC]

Why do teachers and textbooks make it so hard?

1. A stationary point exists when f'(x) = 0.

FIRST DERIVATIVE TEST
If f'(x) changes from - to + then there is a minimum turning point.
If f'(x) changes from + to - then there is a maximum turning point.
If f'(x) doesn't change (or goes + to 0 to + or goes - to 0 to -) then there is a horizontal point of inflection.

SECOND DERIVATIVE TEST
If f"(x) > 0 then there is a minimum turning point (Positive = concave uP)
If f"(x) < 0 then there is a maximum turning point (Negative = concave dowN)

2. A point of inflection exists when f"(x) = 0 AND f"(x) changes sign through the point.

A point to remember when sketching curves ... it's OK to plot points!