is a repeated root a point of inflection or not neccasarily
idk if ive forgotten as level maths but if a polynomial has a repeated root is it valid to deduce at that root there is a point of inflection or not . I undestant point of inflections are involved with the second derivative but in terms of simply just the repeated root is it sufficient to conlude that there exists an POI at the root.
Original post by tovestyre
idk if ive forgotten as level maths but if a polynomial has a repeated root is it valid to deduce at that root there is a point of inflection or not . I undestant point of inflections are involved with the second derivative but in terms of simply just the repeated root is it sufficient to conlude that there exists an POI at the root.
x^2 and x^3 both have repeated roots at x=0 and what can you say about the (stationary) point of inflection (or not)?
See counterexample above.
At best you can say x=a is a repeated root of f(x) is equivalent to f(a)=f'(a)=0.
(I don't know why this is an oddly useful fact if you're doing MAT.)
Inflexion point only cares about a change in sign for f''(x).
(This is also saying we can have non-stationary inflexion points, e.g. f(x)=x(x+1)(x-1) has non-stationary inflexion point at 0.)
At best you can say x=a is a repeated root of f(x) is equivalent to f(a)=f'(a)=0.
(I don't know why this is an oddly useful fact if you're doing MAT.)
Inflexion point only cares about a change in sign for f''(x).
(This is also saying we can have non-stationary inflexion points, e.g. f(x)=x(x+1)(x-1) has non-stationary inflexion point at 0.)
Original post by tovestyre
idk if ive forgotten as level maths but if a polynomial has a repeated root is it valid to deduce at that root there is a point of inflection or not . I undestant point of inflections are involved with the second derivative but in terms of simply just the repeated root is it sufficient to conlude that there exists an POI at the root.
Not necessarily, but a repeated root does imply that the root is also a stationary point (not all points of inflection are stationary)
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