Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Determine the Concavity -- Answer in 20 and get best answer!?
Determine the concavity of the function:
f(x) = 2x^3 - 9x^4 - 108x
Thanks! Answer within twenty minutes and get a best answer!
1 Answer
- 9 years agoFavorite Answer
Take the first and second derivatives
f'(x) = 6x^2 - 36x^3 - 108
f''(x) = 12x -108x^2 = 12x(1-9x)
f''(x) is 0 when x=0 and x=1/9. When x is less than 0, f''(x) is negative. When x is between 0 and 1/9 f''(x) is positive and when x is greater than 1/9, f''(x) is negative.
The concavity test tells us that when f''(x) is positive, the function is concave up. When f''(x) is negative, the function is concave down.
Therefore, f is concave up on (0,1/9) and concave down everywhere else.
