Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. 1. (8pt) consider the function f(x) = (x + 3)(x +

1. (8pt) Consider the function f(x) = (x + 3)(x + 5)^2 √ (7 −...

50.1K

Verified Solution

Question

Basic Math

1. (8pt) Consider the function f(x) = (x + 3)(x + 5)^2 √ (7 − x)whose first and second derivatives are f'(x) = ((x + 5)(139 + 12x −7x^2))/2 √ (7 − x) , f''(x) = (35x^3 − 225x^2 − 843x + 3481)/ 4(7 −x)^3/2 .

Note: 35x 3 − 225x 2 − 843x + 3481 has three roots: x1 ≈ 7.8835,x2 ≈ −4.3531 and x3 ≈ 2.8982.

(a) (1pt) What is the domain of f(x)? (b) (1pt) What are thex-intercepts and y-intercepts of f(x)? (c) (1pt) What are thecritical numbers of f(x)? (d) (1pt) On what open interval(s) isf(x) increasing, and on what open interval(s) f(x) is decreasing?(e) (1pt) What are the x-values of potential points of inflectionof f(x)? (f) (1pt) On what open interval(s) is f(x) concave-upward,and on what open interval(s) f(x) is concave-downward? (g) (2pt)Sketch y = f(x). Clearly label the intercepts, extrema, and pointsof inflection.

Answer & Explanation Solved by verified expert
3.8 Ratings (510 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

Suppose a life insurance company sells a 200 000 1 year term life insurance policy...

Statistics
Q

You are a member of the social sciences research team and are tasked with the following:...

Psychology
Q

How does globalization and automation affect the middle-class, especially in South Korea?

Economics
Q

Leos total bill at the blue lobster came to $45.90. he wanted to leave a...

Basic Math
Q

ASK YOUR TEACHER Ornithologists have determined that some species of birds tend to avoid flights...

Calculus
Q

The capital budgeting process requires four steps to complete: (1) Finding new investment opportunities; (2)...

Accounting
Q

REQUIRED Use the information provided below to prepare the Statement of Changes in Equity of...

Accounting
Q

Net income of \$50,160 was reported, anddividends of \$26,220 were paid in 2025. New equipenent...

Accounting
Q

Suppose that the price p for a certain commodity declines toward $3 as the quantity...

Accounting
Q

Forecasting with the Parsimonious Method and Estimating Share Value Using the DCF Model Following are...

Accounting
Q

John won a lottery that will pay him $450000 at the end of each of...

Accounting
Q

You were assigned by Kirska Holdings to help estimate its cost of capital. You have...

Finance