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Find the critical numbers and stationary points of each of the following functions.$\;f(\theta)=\theta+\sin\theta$ in $[0 , 2\pi ]$

Note: This is part 6 of a 6 part question, split as 6 separate questions here.

1 Answer

  • A ciritical number of a function f is a number c in the domain of f such that either $f'(c)=0$ or $f'(c)$ does not exist.
  • Stationary points correspond to critical numbers for which $f'(c)=0$
$f(\theta)=\theta+\sin \theta$ in $[0,2 \pi]$
Step 1:
$f'(\theta)=1+\cos \theta$
$f'(\theta)=0=>1+\cos \theta=0=>\cos \theta=-1$
$\theta=(2n-1) \pi, n \in z$
Step 2:
$\theta= \pi \in [0,2 \pi]$ is a critical number
When $\theta=\pi\; f(\pi)=\pi+0=\pi$
The critical point is $(\pi,\pi)$
answered Jul 31, 2013 by meena.p

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