If f(x) = frac{sin(x + a)}{sin(x + b)},a neq | vedclass

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(C) Given function is $f(x) = \frac{\sin(x + a)}{\sin(x + b)}$.To find the critical points,we differentiate $f(x)$ with respect to $x$ using the quoti

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Neither maximum nor minimum at $x = 0$.

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(C) Given function is $f(x) = \frac{\sin(x + a)}{\sin(x + b)}$.To find the critical points,we differentiate $f(x)$ with respect to $x$ using the quotient rule:$f'(x) = \frac{\sin(x + b) \cos(x + a) - \sin(x + a) \cos(x + b)}{\sin^2(x + b)}$.Using the trigonometric identity $\sin(A - B) = \sin A \cos B - \cos A \sin B$,we get:$f'(x) = \frac{\sin((x + a) - (x + b))}{\sin^2(x + b)} = \frac{\sin(a - b)}{\sin^2(x + b)}$.Since $a 
eq b$,$\sin(a - b) 
eq 0$. Therefore,$f'(x) 
eq 0$ for any $x$ in the domain.Since the derivative is never zero,the function $f(x)$ does not have any local maxima or local minima at $x = 0$ or anywhere else in its domain.

If $f(x) = \frac{\sin(x + a)}{\sin(x + b)}$,$a \neq b$,then $f$ is......

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