Function f(x) = log_{10} cos x is . . . . . | vedclass

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(B) To determine the nature of the function $f(x) = \log_{10} \cos x$,we find its derivative with respect to $x$.$f'(x) = \frac{d}{dx} (\log_{10} \cos

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decreasing

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(B) To determine the nature of the function $f(x) = \log_{10} \cos x$,we find its derivative with respect to $x$.$f'(x) = \frac{d}{dx} (\log_{10} \cos x) = \frac{1}{\cos x \cdot \ln 10} \cdot (-\sin x) = -\frac{	an x}{\ln 10}$.In the interval $\left(0, \frac{\pi}{2}ight)$,$	an x > 0$ and $\ln 10 > 0$.Therefore,$f'(x) = -\frac{	an x}{\ln 10} Since the derivative is negative in the given interval,the function $f(x)$ is a decreasing function.

Function $f(x) = \log_{10} \cos x$ is . . . . . . function in the interval $\left(0, \frac{\pi}{2}\right)$.

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