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

If #f(x)=sinx-cosx#, what are the critical points on the interval (0,pi)?

Answer 1

Charles Arocha

Critical points are elements of the domain at which #f'(x) = 0# or #f'(x)# does not exist.

For this question the domain of #f(x) = sinx-cosx# is restricted to #(0, pi)#

#f'(x) = cos x +sinx#

#cos x +sinx = 0# where #sinx=-cosx# so #tanx = -1# and between #0# and #pi#, that occurs at #x= (3 pi)/4#

The critical point is #(3 pi)/4#.

(An alternative terminology makes critical points ordered pairs. Under this terminology, the critical point would be: #( (3 pi)/4, sqrt2)#

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Answer 2

Ezra Adams

The critical points of ( f(x) = \sin(x) - \cos(x) ) on the interval ( (0, \pi) ) are ( x = \frac{\pi}{4} ) and ( x = \frac{5\pi}{4} ).

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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.