Finding the Range of Graphs: f(x) = ex2 and g(x) = x2 + 3ex2

[jsmith613]

Homework Statement

f(x) = e^x2
find the range of f(x)
How do I do this - I don't know how to draw this graph?g(x) = x² + 3e^x2
Again, how is this done without drawing the graph?

Homework Equations

The Attempt at a Solution

so for the first graph, for example, I differentiated it
dy/dx for f(x) = 2xe^x2
Giving a min. point of 0
BUT THE ANSWER IS f(x) ≥1
Why does the min point method not work?

 

[jsmith613]

oh of course, I found the x-value that gives the min. point
so I sub this into the original equation
never mind :)