does a curve has only one point of inflection?

Question

when we put second derivative zero , suppose the answer comes x=2 or we have a equation of order >^3 that we will end up with quadratic formula upon solving we get two point on x axis . does this mean we have >1 point of inflection ???????????????????/

Answer 1

Curves of higher order can have more points of inflection.

Ordinarily, a quadratic curve has 0 points of inflection.
A cubic has one point of inflection.
An equation of the fourth order has two points of inflection,
and so on.

Answer 2

A curve has a point of inflection wherever both the first and second derivatives are 0. If it happens at several points, they are all inflection points.

Answer 3

If you set the second derivative equal to zero, your curve will have one inflection point for every solution you found. 3 values for x means three inflection points.

Answer 4

Y= (x^2+ 2x+ 4)^ -a million Y' = -[ (x^2+ 2x+ 4)^-2 ]( 2x+2) = -2(x+a million)/(x^2 + 2x + 4)^2 Y' = 0 mutually as the numerator is 0: x= -a million f(-a million)=a million/3 ---- Y'' =[ (x^2 + 2x +4)^2 * (-2) - (-2x-2) * 2(x^2 +2x + 4)(2x+2)] / (x^2+ 2x+ 4)^4 The numerator= 0 (X^2 +2x +4)[ -2(x^2+ 2x+4) +2* (2x+2)^2 ] = 0 X^2 + 2x+4 is in basic terms no longer waiting to equivalent 0 -2x^2 -4x -8 + 8x^2 +16x +8 = 0 6x^2 +12x = 0 6x(x+2) = 0 X= 0 or x= -2 f(0)= a million/4 f(-2)= a million/4 (0, a million/4) and (-2, a million/4) are inflection components. f '' (-a million)=( -18-0)/80 one= -2/9 because of the reality the 2d by skill of-product is detrimental at (-a million, a million/3) it particularly is a optimal. i desire this facilitates!

Answer 5

If i understand your question correctly, if the second derivative is one number then yes there is only one point of inflection. A positive number indicates an absolute maximum, negative indicates absolute minimum.