Wichtig fürs Abi: Wendestellen berechnen 🎓 #MatheMitNick 👨🏻‍🏫 #Abi24 #Abitur

If you want to calculate the position of the turning point in the abitur, you have to calculate the zero-points of the second derivative. But let's first look at what a turning point is. If this is a road that looks like a helicopter and a car is driving along it, the car first makes a right turn and then goes into a left turn. And where the transition from right to left is, that's where the turning point is. But how do I get it mathematically? I already said that the second derivative is equal to zero and then calculate the zero-points. But first we need the first derivative. Maybe as a repetition, how do I derive this? You bring the exponent forward three times a third is one, I'll write it down now, and then subtract one from the exponent at the top, i.e. x to the power of two. Again, if I want to derive 1.5x², I bring the second one forward again, 2 times 1.5 gives 3. At the top I subtract one again, so I have x to the power of one, I just write x. And if you have something like minus 4x, then you just write minus 4, but it would work with the same law. But now I said we need the zero-points of the second derivative, and we'll do that now. f'' of x, we derive again. The 2 comes forward again and at the top we subtract one, so I only have 2x. From 3x, just 3 and minus 4 is omitted. So, if I want the zero-points now, I have to equate that with zero. So, let's get rid of the 3 first by calculating minus 3 on both sides. We then assume 2x is equal to minus 3. Divide by 2 and we're done. We have found our potential turning point. What is still missing is the y-value for the entire turning point. And we could, for example, use the x-value in the third derivative. And if that is not zero, then we have shown rock-solid that it is a turning point. And that was Abi with Nick.