Sketch the graph of a function f that satisfies all of the given condi-tions.• There is a jump discontinuity at x = -2.• lim f(x) = –∞• lim f(x) = -1X→-00• f'(3) = 0• f'(1) = 1• f'(4) = -2

To sketch a function fx satisfying the following conditions limx→∞fx=-∞limx→-∞fx=-1f'3=0f'1=1f'4=-2…

Answered: Sketch the graph of a function f that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Sketch the graph of a function f that satisfies all of the given condi-
tions.
• There is a jump discontinuity at x = -2.
• lim f(x) = –∞
• lim f(x) = -1
X→-00
• f'(3) = 0
• f'(1) = 1
• f'(4) = -2

Expert Solution

Step 1

To sketch a function $f (x)$ satisfying the following conditions

$\begin{array}{rcl} \underset{x \to \infty}{l i m} f (x) & = & - \infty \\ \underset{x \to - \infty}{l i m} f (x) & = & - 1 \\ f' (3) & = & 0 \\ f' (1) & = & 1 \\ f' (4) & = & - 2 \end{array}$

Also, $f (x)$ has a jump discontinuity at $x = - 2$ . Therefore,

$\underset{x \to 2 +}{l i m} f (x) \neq \underset{x \to 2 -}{l i m} f (x)$

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