University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Section 4.1 - Extreme Values of Functions - Exercises - Page 215: 22

Answer

$f(x)$ has an absolute maximum value of $0$ at $x=-4$ and an absolute minimum value of $-5$ at $x=1$.
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Work Step by Step

$$f(x)=-x-4\hspace{1cm}-4\le x\le1$$ 1) Find the derivative $f'(x)$: $$f'(x)=-1$$ Since the value of $f'(x)$ is constant and equals $-1$, $f(x)$ has no critical points. 2) Evaluate $f(x)$ at the endpoints: - For $x=-4$: $$f(-4)=-(-4)-4=4-4=0$$ - For $x=1$: $$f(1)=-1-4=-5$$ This means the function $f(x)$ has an absolute maximum value of $0$ at $x=-4$ and an absolute minimum value of $-5$ at $x=1$.
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