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The curve is .
Apply derivative on each side with respect to .
.
Again apply derivative on each side with respect to .
.
Find the inflection points.
Equate to zero.
and
Solve for .
The general formula for finding the roots of a quadratic equation is .
The inflection points at and .
Substitute in the function.
Substitute in the function.
Substitute in the function.
Therefore the inflection points are , and .
Consider the two points are and .
Find the slope between the two points.
Now consider the two points are and .
Find the slope between the two points.
Observe the two slopes, the slopes are equal.
Therefore the inflection points are lie in a same straight line.
The inflection points are lie in a same straight line.
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