How would you arrange the steps in order in a continuous, 2x differentiable function when finding inflection?

Question

QUESTION:
How would you arrange the steps in order in a continuous, twice differentiable function when finding its inflection point?

THE CHOICES IN RANDOM ORDER:

A = evaluate the function at the points where the second derivate is zero
B = analyze the sign changes of the second derivative
C = find the zeors of the second derivative
D = find the second derivative
E = find the first derivative

Whats the proper order A through E?

Thanks!

...are you sure? Everyone agrees with him?

Answer 1

EDCBA
Follow all the steps from bottom to top

Edit:
The second derivative is the derivative of the first derivative. So you need to do E before D. A,B and C require the second derivative. SO A,B and C must all come later than D and therefore E also. To do step B, you need to know where the sign change occurs (at zeroes). So B comes after C.
Step A needs the zeroes of the 2nd derivative. So A must come later than C.

You could possibly do A before B, but that would make slightly more work. You could evaluate the function at all the critical points then determine which ones are inflection points. But if you find which critical points are inflection points by doing step B first, you may not need to evaluate the function at all of the critical points.

Answer 2

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