What are the values and types of the critical points, if any, of $f (x) = ∣ ∣ x^{2} - 1 ∣ ∣$ $f(x) = abs(x^2-1)$ ?

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What are the values and types of the critical points, if any, of $f (x) = ∣ ∣ x^{2} - 1 ∣ ∣$ $f(x) = abs(x^2-1)$ ?

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Answer 1 · 2016-11-07T00:21:27

The critical numbers are $- 1$ $-1$ and $1$ $1$ where $f'(x)$ does not exist.

Explanation:

Depending on the terminology you are using that might make the critical points $-1$ and $1$ , or you might have been taught to say they are $(-1,0)$ and $(1,0)$ .

Note that $f(x) >=0$ for all $x$ .

Both $f(-1)$ and $f(1)$ are $0$ , so both are locations of the absolute minimum.

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What are the values and types of the critical points, if any, of $f (x) = ∣ ∣ x^{2} - 1 ∣ ∣$ $f(x) = abs(x^2-1)$ ?

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Explanation:

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What are the values and types of the critical points, if any, of f(x) = abs(x^2-1)f(x)=∣∣x2−1∣∣f(x) = abs(x^2-1)?

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Explanation:

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What are the values and types of the critical points, if any, of $f (x) = ∣ ∣ x^{2} - 1 ∣ ∣$ $f(x) = abs(x^2-1)$ ?