Locating critical points Find the critical points of the follo...

Question

Locating critical points Find the critical points of the following functions. Assume a is a nonzero constant.

ƒ(x) = x³ -4a²x

Accepted Answer

Welcome back everyone. Determined the X coordinates of the critical points of the function F of X equals x cub minus 6BX where B is a constant and B is not equal to 0. So first of all, we're given our function F of X equals x cubed minus 6BX. Now, let's understand that it's defined for all acts, right? Because it's a polynomial. So its domain is all real numbers. We can say that the domain is X belongs to all rail numbers. Now to find the critical points, our first step is to identify the derivative, and we can see that using the power rule, the derivative of X cube is 3 x squared. The derivative of axis 1, so we are subtracting the constant 6B. Now this is again a polynomial, so it's defined for all X, meaning we don't need to check when the derivative does not exist in the domain of the function. What we're going to do is check the second condition when F of X is equal to 0. So this means that we are checking when 3 X2 minus 6B is equal to 0. Let's factor it out. We are going to have 3 x 2 minus 2 B is equal to 0. So that X2 minus 2B must be equal to 0. We can rewrite it as x2 minus square root of 2b2 equals 0 because now we can apply the difference of squares factorization. So x minus square root of 2b multiplied by x plus square root of 2 b. Is equal to 0. So we have 2 factors. The product of 2 factors is equal to 0. This implies that either the first factor is equal to 0, so that x. is equal to square root of 2b or the second factor is equal to 0 so that x is negative square root of 2b. So we have two critical points, right? Specifically, we are given the coordinates of those critical points. So X is either positive or negative square root of 2 B. Thank you for watching.

Locating critical points Find the critical points of the following functions. Assume a is a nonzero constant.ƒ(x) = x³ -4a²x

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Locating critical points Find the critical points of the following functions. Assume a is a nonzero constant.

ƒ(x) = x³ -4a²x