So given that, let's now find g prime of x. G prime of x is going to be equal to, I'm just gonna apply the power rule multiple times, four times 1 4th is just one, I'm not even gonna write the one down, it's gonna be one times x to the four minus one power. So four to the 3rd power minus three times four is 12, x to the three minus one power, or x to the 2nd power, plus two times 24, or 48, x to the two minus one, or x to the 1st power, I could just write that as x. So there you have it, I have our first derivative, now we wanna find our second derivative. So g prime prime of x is just the derivative of the first derivative with respect to x, and so more of the power rule, three x squared minus 24 x to the first, or just 24 x, plus 48. So let's think about where this switches signs. And this is a continuous function, it's going to be defined for all x's, so the only potential candidates of where it could switch signs are when this thing equals zero. So let's see where it equals zero.