Question

f(x)= sin x is the equation with intervals x={pi/4 , 7pi/4 }...... den locations of local minima are ??

Answer 1

Any point can be a local extreme on the right interval. However, an absolute minimum does occur on this interval. Finding where the derivative of f (cos x) is zero or undefined on this interval\[\cos \frac{ \pi }{ 2 }=0 \]and\[\cos \frac{ 3\pi }{ 2 }=0\]Substute pi over 2 and 3 pi over two into the sine function, we find that\[\sin \frac{ \pi }{ 2 }=1\]but\[\sin \frac{ 3\pi }{ 2 }=-1\] So 3 pi over two is the minimum