Home > Calculus > Identifying Stationary Points (Critical Points) for a Function

What are the critical values, if any, of # f(x)= sin^2x +cos^2x in [0,oo]#?

Answer 1

I'd say that every number in #[0,oo)# is a critical value.

#f(x) = sin^2x+cos^2x = 1#

So #f'(x) = 0#

The critical values of #f# are the numbers in the domain of #f# at which the derivative either does not exist or the derivative is #0#. Since the derivative is #0# for all numbers in the domain, I would say that every number in the domain is a critical value.

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Answer 2

Luke Alvarez

The critical values of ( f(x) = \sin^2(x) + \cos^2(x) ) in the interval ([0, \infty)) are not applicable because ( f(x) ) is a constant function equal to 1 for all values of ( x ) within the given interval.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.