Consider the following function: where f(x) = 2x²x³ +1 x E (a) Find the x that are critical value points of f(x) (values of x that are a potential mini- mum or maximum). (b) Are those critical values maximum or minimum? (Hint: Check the second order derivative. Check also the value of the function at the endpoints -1 and to make sure you have the correct answer.)

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Consider the following function:
where
f(x) = 2x² — x³ + 1
€ [-1, 3]
x
(a) Find the x that are critical value points of f(x) (values of x that are a potential mini-
mum or maximum).
(b) Are those critical values maximum or minimum? (Hint: Check the second order
derivative. Check also the value of the function at the endpoints -1 and ½ to make
sure you have the correct answer.)
Transcribed Image Text:Consider the following function: where f(x) = 2x² — x³ + 1 € [-1, 3] x (a) Find the x that are critical value points of f(x) (values of x that are a potential mini- mum or maximum). (b) Are those critical values maximum or minimum? (Hint: Check the second order derivative. Check also the value of the function at the endpoints -1 and ½ to make sure you have the correct answer.)
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