Find all the critical points of the function y = h(x) = In(x + 1)6 – 2x + 5. Order the critical points from the smallest to the largest and fill in the blanks below with information about each critical point, starting with the smallest. Express each number as a fraction reduced to its simplest form (e.g., -5/1 or 0/1). Put X in all redundant blanks. For example, if you found only 2 critical points, you would fill all the blanks for Critical point 3 with X.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
Question
Find all the critical points of the function
y = h(x) = In(x + 1)6 – 2x + 5.
Order the critical points from the smallest to the largest and fill in the blanks below
with information about each critical point, starting with the smallest. Express each
number as a fraction reduced to its simplest form (e.g., -5/1 or 0/1). Put X in all
redundant blanks. For example, if you found only 2 critical points, you would fill all
the blanks for Critical point 3 with X.
Critical point 1 (the smallest critical value):
a) The value of Critical point 1 is equal to
2
b) In the next blank fill in "max", "min", or "inflection" (without the quotation marks).
Critical point 1 is a
max
c) Does the second derivative test imply that Critical point 1 is a global maximum or
a global minimum? Answer Yes or No:
no
Critical point 2:
a) The value of Critical point 2 is equal to
b) In the next blank fill in "max", "min", or "inflection" (without the quotation marks).
Critical point 2 is a
c) Does the 2nd derivative test imply that Critical point 2 is a global maximum or a
global minimum? Answer Yes or No:
no
Critical point 3:
a) The value of Critical point 3 is equal to
b) In the next blank fill in "max", "min", or "inflection" (without the quotation marks).
Critical point 3 is a
c) Does the 2nd derivative test imply that Critical point 3 is a global maximum or a
global minimum? Answer Yes or No:
no
Transcribed Image Text:Find all the critical points of the function y = h(x) = In(x + 1)6 – 2x + 5. Order the critical points from the smallest to the largest and fill in the blanks below with information about each critical point, starting with the smallest. Express each number as a fraction reduced to its simplest form (e.g., -5/1 or 0/1). Put X in all redundant blanks. For example, if you found only 2 critical points, you would fill all the blanks for Critical point 3 with X. Critical point 1 (the smallest critical value): a) The value of Critical point 1 is equal to 2 b) In the next blank fill in "max", "min", or "inflection" (without the quotation marks). Critical point 1 is a max c) Does the second derivative test imply that Critical point 1 is a global maximum or a global minimum? Answer Yes or No: no Critical point 2: a) The value of Critical point 2 is equal to b) In the next blank fill in "max", "min", or "inflection" (without the quotation marks). Critical point 2 is a c) Does the 2nd derivative test imply that Critical point 2 is a global maximum or a global minimum? Answer Yes or No: no Critical point 3: a) The value of Critical point 3 is equal to b) In the next blank fill in "max", "min", or "inflection" (without the quotation marks). Critical point 3 is a c) Does the 2nd derivative test imply that Critical point 3 is a global maximum or a global minimum? Answer Yes or No: no
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