Find and classify the critical points off(x) = 4x³(6 - x)6 as local maxima and minima. Critical points: a = 0,741586.35924 Classifications: min, max (Enter your critical points and classifications as comma-separated lists, and enter the types in the same order as your critical points. Note that you must enter something in both blanks for either to be evaluated. For the types, enter min, max, or neither.
Find and classify the critical points off(x) = 4x³(6 - x)6 as local maxima and minima. Critical points: a = 0,741586.35924 Classifications: min, max (Enter your critical points and classifications as comma-separated lists, and enter the types in the same order as your critical points. Note that you must enter something in both blanks for either to be evaluated. For the types, enter min, max, or neither.
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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Transcribed Image Text:Find and classify the critical points off(x) = 4x5(6 − x)6 as local maxima and minima.
Critical points: x = 0,741586.35924
Classifications: min, max
(Enter your critical points and classifications as comma-separated lists, and enter the types in the same order as
your critical points. Note that you must enter something in both blanks for either to be evaluated. For the types,
enter min, max, or neither.
Expert Solution
Step 1
Given function as f(x) = 4x ^ 5 * (6 - x) ^ 6 Now find Critical points as minimum values as putting f(x) = 4x ^ 5 * (6 - x) ^ 6 = 0
then we get x ^ 5 * (6 - x) ^ 6 = 0 or
x ^ 5 = 0, 5 * (6 - x) ^ 6 = 0 or
x = 0 and x = 6
Critical Values x = 0.6
Now find Maximum values as keeping f(x)= 0
f(x prime)= d * (4x ^ 5 * (6 - x) ^ 6)/(dx) = 0
4x ^ 5 * (6 * (6 - x) ^ 5) + (6 - x) ^ 6 * (20x ^ 4) = 0
(4x^ 4 )(6-x)^ 5 [ (6x + (6 - x)(5)] = 0
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