Determine the critical points of the function $f(x) = x^4 - 4x^2 + 3$.

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∻Solution by Steps∻ ‖ step 1 ⋮ To determine the critical points of the function $f(x) = x^4 - 4x^2 + 3$, we first need to find its derivative. ‖ ‖ step 2 ⋮ The derivative of $f(x)$ is $f'(x) = \frac{d}{dx}(x^4 - 4x^2 + 3)$. ‖ ‖ step 3 ⋮ Calculating the derivative, we get $f'(x) = 4x^3 - 8x$. ‖ ‖ step 4 ⋮ To find the critical points, we set the derivative equal to zero: $4x^3 - 8x = 0$. ‖ ‖ step 5 ⋮ Factor the equation: $4x(x^2 - 2) = 0$. ‖ ‖ step 6 ⋮ Solve for $x$: $4x = 0$ or $x^2 - 2 = 0$. ‖ ‖ step 7 ⋮ This gives us $x = 0$ or $x = \pm \sqrt{2}$. ‖ ∻Answer∻ ⚹ The critical points of the function $f(x) = x^4 - 4x^2 + 3$ are $x = 0$, $x = \sqrt{2}$, and $x = -\sqrt{2}$. ⚹ ∻Key Concept∻ ⚹Critical Points⚹ ∻Explanation∻ ⚹Critical points of a function occur where its derivative is zero or undefined. In this case, we found the derivative, set it to zero, and solved for $x$ to find the critical points.⚹◊What is the formula for finding critical points in a polynomial function?⍭ Generate me a similar question◊

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