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I was messing around with my TI 36X Pro and discovered that it is possible to take the 2nd derivative of a function, make tables of a second derivative, and solve a second derivative in the num-solve app. In table edit mode and algebraic entry mode, enter nDervi (your function, x,x). Go to num-solve and set it up as 0=nDerive( press table, hit choice 1 which will enter f(x into the numsolve equation, complete the parentheses, and make the right side |x=x. Press enter, enter a suitable guess, and you will find the value of x where an inflection point lies.

Alas, while this works for finding 2nd derivative = for functions like sin(x) or sin(x)^2, I get an invalid domain error for functions such as x^4-4*x^3. If anyone figures out why this is the case, please post.

I have not run into a problem yet with finding zeros for first derivatives to find a max or min of f(x) for any function that takes less than 80 characters to enter.