So let's study our second derivative. In order to study our second derivative, let's find it. So we know that g of x is equal to 1 4th x to the 4th minus four x to the 3rd power plus 24 x squared. 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.