SOLUTION: Hi, I'm trying to find the absolute minimum and maximum values of {{{ f(x) = e^(-x^2) }}} when {{{ -4 <= x <= 3 }}}. I started by finding the derivative, but I'm struggling when I

Algebra ->  Graphs -> SOLUTION: Hi, I'm trying to find the absolute minimum and maximum values of {{{ f(x) = e^(-x^2) }}} when {{{ -4 <= x <= 3 }}}. I started by finding the derivative, but I'm struggling when I       Log On


   

Question 1153545: Hi, I'm trying to find the absolute minimum and maximum values of +f%28x%29+=+e%5E%28-x%5E2%29+ when +-4+%3C=+x+%3C=+3+. I started by finding the derivative, but I'm struggling when I set the derivative equal to 0. I can find decimal values with my calculator, but need the exact form. Can someone walk me through it?
Thanks!!
Answer by ikleyn(52876) About Me  (Show Source):
You can put this solution on YOUR website!

graph%28+330%2C+330%2C+-5%2C+5%2C+-2%2C+2%2C%0D%0A++++++++++e%5E%28-x%5E2%29%0D%0A%29


       Plot y = e^(-x^2)



From the plot, you can see that  e^(-x^2)  is an even function (which is very clear from the formula).


First derivative is  -2x*e^(-x^2), and when you equate it to zero, you easily will find the critical point x= 0.