Calculus question

Question

Use the function y = 2e^-5x^2 to answer each question. Help!?

1. Discuss the symmetry of the graph.
2. Determine the intervals of increase and decrease

Answer 1

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).