Here. We have to function after box is equal to one minus X to the two thirds power on the closed in developed from negative 8 to 8. So we first take the derivative of our function So f prime off X while we take throughout the term. By term, we have a fractional exponents. You okay? Right. So the derivative here is just Well, we just get to third X to the two thirds minus one. That's two thirds minus three therapists. Negative. One third. Right. Um, so, aan den times when you have a native born here in front, therefore the derivative of Prime of X is gonna be equal to negative two thirds X to the negative one third. Okay, so there's a derivative now find the critical values. We just take a negative, and we set it equal to zero. So if we do this, Well, this was just imply, right? We could if we want to mean much, play both sides By what native three halves that's gonna cancel out the coefficient on the X, but still make it zero. All right. And then we have actually one third, um, equals zero. That that's still that implies that X is equal to zero. So this may look a little scary, but it's really not because we just get here. That X is equal to zero. Those are critical value. Okay, so we list out all critical values and endpoints. So we have a negative eight is the one end point, then the critical value of zero and the other end point of eight. Now we evaluate our original function at those values. So let's do F zero first. So f zero is equal. Talk about one minus zero, which is equal to one. So f zero is equal toe one and then do f of negative eight. So f off. Negative. Eight. Well, that's equal to one minus negative. Eight to the two thirds. Um, okay. The cube root of negative eight, which is, um, two and a few square it. Get four. This is what you just get. One minus four, which is native three. So f of negative eight is negative. Three and f of eight. Well, we get one minus 8 to 2 thirds. So again, 8 to 2 thirds is the cube root of eight squared. That's four. So, again, we get one minus fork. So again we get half of eight is also equal to negative three. So not to find the absolute max and men. So over the interval, native 8 to 8 or the absolute maximum is the largest output. And we see that is the only positive value, which is one right. So the absolute max is equal to one, and it occurs when X is equal to zero. So that X equal to zero now for the absolute men. Yeah, well, that's the smallest output is negative. Three, right? We absolutely men is negative. Three. But what is it occurred? Where the coach at two values right that occurs at X, being equal to negative eight. Okay. And also right and also x be equal fate.