What are the extrema of #f(x) = e^(-x^2)# on #[-.5, a] #, where #a > 1 #?
f(x) > 0. Maximum f(x) isf(0) = 1. The x-axis is asymptotic to f(x), in both directions.
f(x) > 0.
Using function of function rule,
At x = 0, y' = 0 and y'' < 0.
So, f(0) = 1 is the maximum for f(x), As required, .
x = 0 is asymptotic to f(x), in both the directions.
Interestingly, the graph of