The paper on which it came had $4$ choices of answer, out of which $2$ options are creating confusion.
For the function $f(x) = sin(x)$ in the interval $x\in[\frac{\pi}{4},\frac{7\pi}{4}]$, the number and location(s) of the local minima of the function is(are) ?
$i)\ \ 1\ at\ \frac{3\pi}{2}$
$ii)\ \ 2\ at\ \frac{\pi}{4} and\frac{3\pi}{2}$
According to me option $(ii)$ should be the right choice. But I'm not sure. Can anyone help ?
You can think of a local minima as being a point on the graph where you can draw an arbitrarily small circle around the point and every point in the graph that is in the circle will be larger than the proposed minima. In the case where a minima is an end point, all that we examine is the side of the graph inside the interval we care about. The main idea here is that an endpoint can be a local extrema.
So $\pi/4$ and $3\pi/2$ give us our two local minima.