Alternating roots of $f(x) = \exp(x) \sin(x) -1$ and $\exp(x)\cos(x) +1$
Solution 1:
The functions $g(x)=\sin(x)-\exp(-x)$ and $g'(x)=\cos(x)+\exp(-x)$ have the same roots as the given functions. Thus the problem reduces to the theorem of Rolle.
The functions $g(x)=\sin(x)-\exp(-x)$ and $g'(x)=\cos(x)+\exp(-x)$ have the same roots as the given functions. Thus the problem reduces to the theorem of Rolle.