Show that the equation
x^2*e^mod(x)
Has at least two solutions for x in
-1<=x<=1.
Thanks
Note that this is the same as showing $\displaystyle x^2 e^{|x|} - 2 = 0$ at least twice in the given range.
Let $\displaystyle f(x) = x^2 e^{|x|} - 2$ (note that it is a continuous function) and consider $\displaystyle f(-1),~f(0), \text{ and }f(1)$ and apply the intermediate value theorem.
Well I ahve found out that the theorem is as follows:
If ƒ(x) is a continuous real-valued function on the closed interval from a to b, then, for any y between the least upper bound and the greatest lower bound of the values of ƒ, there is an x between a and b with ƒ(x) = y
Now how do I apply this to the question.