Find out all the critical points for the function.

Solution

Following is the derivative for this function.

Now, this looks unpleasant, though along with a little factoring we can clean things up a little as follows,

This function will present everywhere and thus no critical points will come from that. Finding out where it is zero is easier than it looks.  We know that exponentials are never zero & therefore the only way the derivative will be zero is if,

1 - 2t ²  = 0

1 = 2t ²

1 /2 = t ²

We will contain two critical points for this function.

t =  1/√2