Applying the product rule,
By the chain rule,
Which simplifies into
Which can also be written as
So your derivative was wrong in the first place. Might be why your answer was coming up wrong
Im having trouble with finding the minimum value.
the function is (x)(e^5/x)
my derivative is (e^5/x)(-5x+1)
I set the derivative to 0 and get
Plugging this back into the original equation gets me
14400979867.5...which is wrong. Any help would be appriciated
Actually won't make f'(x) = 0.
Plugging in x = 0,
Which is clearly undefined. So, as you've said, x = 5 is your only critical point.
Now, taking the second derivative,
It is readily verified that this function is only concave upwards, so there is only an absolute min.