Consider the function f(x) =x²+8x+15=x+1a. Find the first derivative. f'(x)b. List any critical values.c. Identify intervals of increase.d. Identify intervals of decrease.e. Find the second derivaitve. f'(x)f. Based on parts b through e, f(x) has a maximum of ywhen xwhen x=g. Based on parts b through e, f(x) has a minimum of yh. Use the second derivative to identify intervals where f(x) is concave up..i. Use the second derivative to identify intervals where f(x) is concave down.j. Use the second derivative to find any inflection points.k. State any vertical asymptotes.L. State any slant asymptotes.esc- 2Submit Question!17@# 372୪$E44%0150MacBook Pro66&277

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x²+8x+15 Consider the function f(x): = x+1 a. Find the first derivative. f'(x)= b. List any critical values. c. Identify intervals of increase. d. Identify intervals of decrease.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 8CR

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Question

Consider the function f(x) =
x²+8x+15
=
x+1
a. Find the first derivative. f'(x)
b. List any critical values.
c. Identify intervals of increase.
d. Identify intervals of decrease.
e. Find the second derivaitve. f'(x)
f. Based on parts b through e, f(x) has a maximum of y
when x
when x=
g. Based on parts b through e, f(x) has a minimum of y
h. Use the second derivative to identify intervals where f(x) is concave up..
i. Use the second derivative to identify intervals where f(x) is concave down.
j. Use the second derivative to find any inflection points.
k. State any vertical asymptotes.
L. State any slant asymptotes.
esc
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Step 1: Define the problem

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Step 2: Calculate the derivative of function

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Step 3: Calculate the critical values

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Step 4: Calculate sign table of f'(x)

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Step 5: Calculate the interval of increase

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Step 6: Calculate the interval of decrease

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