Calculus second derivative test and inflection points?

The second derivative test is a way to determine whether a critical value (found from first derivative equals zero) is a local maximum, local minimum or point of inflection.

If dy/dx = 0 and d2y/dx2 > 0 then the point is a local minimum.

If dy/dx = 0 and d2y/dx2 < 0 then the point is a local maximum.

If dy/dx is NOT 0 and d2y/dx2 = 0 then it is a point of inflection.

The difficult case is dy/dx = 0 and d2y/dx2 = 0. This is USUALLY a horizontal point of inflection but there are rare exceptions when it can be a local maximum or local minimum, e.g. y = x^4 at the origin.

x^2-2x-3 on the grounds which you hit upon the spinoff of f(x) shall we take out what does not have an x x^2 - 2x now you incredibly basically diverse the skill to the front and then minus the skill by way of a million so it would be 2x^a million - 2 this is the 1st spinoff. then you definately basically repeat the technique for the 2nd spinoff. 2 may be the 2nd spinoff on the grounds that a million situations 2 = 2 and x^a million - a million = x^0 and -2 has no x so which you eliminate it. ---- x^3 - 3x + a million x^3 - 3x 3x^2 - 3 <<< this is the 1st spinoff 2nd spinoff may be 6x on the grounds which you multiply 2 situations the front this is 3.