When working out if a point is a max min or point of inflection, and the answer for the second diverative is 0 then you use the 3rd deverative and its still zero what kind of point is it??
When working out if a point is a max min or point of inflection, and the answer for the second diverative is 0 then you use the 3rd deverative and its still zero what kind of point is it??
thanks for the help in advance
If the third derivative is 0, we can't make any conclusions about the kind of point it is.
at a local maximum, y' = 0 and y'' is negative at a local minimum, y' = 0 and y'' is positive
30x^5+60x^4 = 0 when x = -2 or x = 0 at x = -2, y'' = about 500 so it is a local minimum at x = 0, y'' = 0 so it seems to be a point of inflection go back to original curve to check what is going on at x=0 at x=0, you have the middle of a very drawn-out point of inflection, since at x=-1 the gradient is positive and at x=1 gradient is also positive
conclusion x=-2 is local minimum x=0 is point of inflection
at a local maximum, y' = 0 and y'' is negative at a local minimum, y' = 0 and y'' is positive
30x^5+60x^4 = 0 when x = -2 or x = 0 at x = -2, y'' = about 500 so it is a local minimum at x = 0, y'' = 0 so it seems to be a point of inflection go back to original curve to check what is going on at x=0 at x=0, you have the middle of a very drawn-out point of inflection, since at x=-1 the gradient is positive and at x=1 gradient is also positive
conclusion x=-2 is local minimum x=0 is point of inflection
When working out if a point is a max min or point of inflection, and the answer for the second diverative is 0 then you use the 3rd deverative and its still zero what kind of point is it??
thanks for the help in advance
use the first differential method if your second derivative is 0 examsolutions made a video on this