For the function $$f(x) = {e^{\cos x}}$$, Rolle's theorem is

$$f(x) = \left\{ {\matrix{ {0,} & {x = 0} \cr {x - 3,} & {x > 0} \cr } } \right.$$

The function f(x) is

The function f(x) = ax + b is strictly increasing for all real x if

Consider a function $f(x)$ which has exactly two roots at $x=a$. If $\mathop {\lim }\limits_{x \to a}\left(\frac{\lambda f^{\prime}(x)}{f(x)}-\frac{1}{x-a}\right)=m(\neq 0)$, then the value of $\lambda$ ix