00:01
For this question, we're asked to find the critical numbers of this function, g of x equals the third root of quantity 4 minus x squared.
00:09
So the critical numbers are the x values for which there may be a max or a min of the function or a point of inflection.
00:17
You find them by finding the points where the first derivative of the function is equal to zero or undefined.
00:24
So the first thing we do is we take the derivative of this function, which is g prime, of x equals derivative of 4 minus x squared to the 1 third.
00:43
So to find this derivative, we would use the power rule, as well as the chain rule, because we need the derivative of this inside quantity.
00:54
So first, g prime of x equals power rule, one third, four minus x squared to the minus two -thirds times the derivative of the inside again, which is minus 2x.
01:13
So this equals minus 2x over 3 times 4 minus x squared to the 2 thirds, because the negative exponent we put in the denominator there.
01:30
So to find the critical numbers, we find where this here is equal to 0 or, undefined.
01:43
So when it's equal to zero, the numerator would be equal to zero...