How many points of inflection are there on x^3+6x-8=0?

To answer this, you take the second derivative of the function, set it equal to zero and solve for x.

f' = 3x^2 + 6

f'' = 6x

Set f '' = 0

6x = 0

x = 0

There is one inflection point and it occurs at x = 0.

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