Find the critical numbers of f (x)= . Explain your reasoning. Find f' (x) and determine where it is undefined or equals zero. In this case, f' (x) has a fractional form.

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Find the critical numbers of f (x) = . Explain your reasoning.
z²+1
O Find f' (x) and determine where it is undefined or equals zero.
In this case, f' (x) has a fractional form.
Its numerator never equals zero, so f' (x) never equals zero.
However, the denominator of f' (x) equals zero when a = 1, –1, making f' (x) undefined.
In conclusion, the critical numbers are 1, –1.
O Find f' (x) and determine where it is undefined or equals zero.
In this case, f' (x) has a fractional form.
However, its denominator never equals zero, so f' (x) is never undefined.
Examining the numerator, we find that f' (x) = 0 when æ = 1, –1.
In conclusion, the critical numbers are –1, 1.
Find f' (x) and determine where it is undefined or equals zero.
In this case, f' (x) has a fractional form.
Its denominator equals zero when x =1,–1, making f' (x) undefined.
Moreover, when = 0 the numerator is zero, making f' (x) equal zero.
In conclusion, the critical numbers are 0, –1, 1.
Transcribed Image Text:Find the critical numbers of f (x) = . Explain your reasoning. z²+1 O Find f' (x) and determine where it is undefined or equals zero. In this case, f' (x) has a fractional form. Its numerator never equals zero, so f' (x) never equals zero. However, the denominator of f' (x) equals zero when a = 1, –1, making f' (x) undefined. In conclusion, the critical numbers are 1, –1. O Find f' (x) and determine where it is undefined or equals zero. In this case, f' (x) has a fractional form. However, its denominator never equals zero, so f' (x) is never undefined. Examining the numerator, we find that f' (x) = 0 when æ = 1, –1. In conclusion, the critical numbers are –1, 1. Find f' (x) and determine where it is undefined or equals zero. In this case, f' (x) has a fractional form. Its denominator equals zero when x =1,–1, making f' (x) undefined. Moreover, when = 0 the numerator is zero, making f' (x) equal zero. In conclusion, the critical numbers are 0, –1, 1.
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