For what value of lambda is the function f(x) | vedclass

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(D) function $f(x)$ is strictly increasing if $f'(x) > 0$ for all $x \in \mathbb{R}$.Given $f(x) = \lambda x + \cos x$.Differentiating with respect to

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$\lambda > 1$

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(D) function $f(x)$ is strictly increasing if $f'(x) > 0$ for all $x \in \mathbb{R}$.Given $f(x) = \lambda x + \cos x$.Differentiating with respect to $x$,we get $f'(x) = \lambda - \sin x$.For $f(x)$ to be strictly increasing,we require $f'(x) > 0$,which means $\lambda - \sin x > 0$,or $\lambda > \sin x$ for all $x$.Since the maximum value of $\sin x$ is $1$,for $\lambda > \sin x$ to hold for all $x$,we must have $\lambda > 1$.

For what value of $\lambda$ is the function $f(x) = \lambda x + \cos x$ strictly increasing?

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