Make a sign diagram for the derivative of the function.f(x) = x +4x³8x² +62f'(x)increasedecreasex =Sketch the graph of the function.yO-4f'(x)Find all open intervals of increase and decrease. (Enter your answers using interval notation.)-2-250-50y050f'(x)AN4-4-2-50x =2f'(x)0f'(x)y50-50yJAALX4-4502-50x =2f'(x)40X

Answered: Make a sign diagram for the derivative…

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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Related questions

Question

Make a sign diagram for the derivative of the function.
f(x) = x +4x³8x² +62
f'(x)
increase
decrease
x =
Sketch the graph of the function.
y
O
-4
f'(x)
Find all open intervals of increase and decrease. (Enter your answers using interval notation.)
-2
-2
50
-50
y
0
50
f'(x)
AN
4
-4
-2
-50
x =
2
f'(x)
0
f'(x)
y
50
-50
y
JAAL
X
4
-4
50
2
-50
x =
2
f'(x)
4
0
X

Expert Solution

Step 1

Introduction:

Any interval in the domain of a function's derivative can be utilized to assess whether the function is increasing or decreasing. The function is said to be rising on I if $f' (x) > 0$ at each point in the interval I. It is claimed that a function is declining on an interval I if $f' (x) < 0$ at every point in the interval. The derivative must be positive or negative at all other locations where the function exists since it is zero or does not exist only at the crucial points of the function.