`g(x) = x^4 - 8x^2` Find the critical numbers of the function.

Textbook Question

Chapter 3, 3.1 - Problem 12 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the critical numbers of the function and for this reason, you must differentiate the function with respect to x, such that:

`f'(x) = (x^4 - 8x^2)'`

`f'(x) = 4x^3 - 16x`

You need to solve for x the equation f'(x) = 0:

`4x^3 - 16x= 0`

Factoring out 4x yields:

`4x(x ^2 - 4) = 0=> 4x = 0 or x ^2 - 4 = 0`

`4x = 0=> x = 0`

`x ^2 - 4 = 0=> (x - 2)(x +2) = 0 => x = 2` and `x = -2`

Hence, evaluating the critical values of the given function, yields x = 0, x = 2 and x = -2.

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