Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.4 Exercises - Page 352: 21

Answer

See graph
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Work Step by Step

→ The function is even, i.e. $f(x) = f(-x)$. What it means for the graph is that it's symmetric with respect to y=axis. → $\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} f(-x)=0 $ → The y-intercept is $y=f(0)=e^{-0^2} = 1$ → The function derivative $(-2xe^{-x^2})$ is positive for negative values of $x$, zero at $x=0$ and negative at positive values of $x$. Thus the graph rises from zero from the far left corner, rises up to 1 at x=0, and gradually approaches the x-axis again.
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