Show that the equation x^4 + 2x^2 − 2 = 0 has exactly one solution on [0, 1]?
First of all, let's compute
If we compute the derivative
We can see that it is always positive in
So, our function starts below the
If a continuous line starts below the axis and ends above, it means that it must have crossed it somewhere in between. And the fact that the derivative is always positive means that the function is always growing, and so it can't cross the axis twice, hence the proof.