
Doug C. answered 09/06/17
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Hi Don,
If this is written as f(x) = 2e-5x^2, then you can ask the question does f(x) = f(-x). If so this is an even function and is symmetric about the y-axis.
Find f'(x) to determine increasing/decreasing. f'(x) = -20xe-5x^2. This will only equal 0 when x = 0. To the left of 0 f' is positive so f is increasing from -inf to 0. To the right of 0 f' is negative so f is decreasing on 0,inf.
See this graph to get the idea: https://www.desmos.com/calculator/lsyjn5whwk
Enable k(x) to see that it is identical to f(x).