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

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Answer 1 · 2015-04-13T15:53:37

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: $( (3 pi)/4, sqrt2)$

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