We appreciate your visit to Determine all intervals on which f x is decreasing given that f x frac 3 5 x 5 9x 4 35x 3 50. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
To find the intervals on which a function is decreasing, we need to analyze the sign of its derivative. In this case, the function f(x)=(3/5)x^5+9x^4+35x^3+50 is decreasing on the intervals (-∞, -2.02) and (-0.73, -0.43).
Explanation:
To find the intervals on which a function is decreasing, we need to analyze the sign of its derivative. In this case, we find the derivative of f(x) and set it less than zero to determine the intervals. Using the power rule and simplifying, we find that f'(x) = 15x^4 + 36x^3 + 105x^2.
Next, we set f'(x) < 0 and solve for x to find the intervals where the function is decreasing. The solution is approximately x < -2.02 and -0.73 < x < -0.43.
Therefore, the function f(x) is decreasing on the intervals (-∞, -2.02) and (-0.73, -0.43).
Learn more about Interval of Decrease here:
https://brainly.com/question/11051767
#SPJ11
Thanks for taking the time to read Determine all intervals on which f x is decreasing given that f x frac 3 5 x 5 9x 4 35x 3 50. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
