Integration of f '' and f ' and determination of the constants:
Find
if
,
, and ![]()
We have the second derivative of the curve, so we can integrate with the General Power rule for integrals
to find the first derivative:
.
In order to determine a value for C1, we can use the value of the first derivative at the given value of x:
. From this we find
. Combining these results, we get ![]()
Now we can integrate again to get the function:

We can determine the unknown constant from the given information:
, or
.
Finally we can combine these results to get
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