Comments

• Not enough information. In addition to being differntiable on an open interval, f must also be continuous on a closed interval. Otherwise you can find counterexamples such as the one above. Given continity and differntiability, this follows from …

  in abstract math problem..? Comment by joni-danerd June 2021
• First use the product rule and you get x'cos^2x + x(cos^2x)' x' = 1, and apply the chain rule on the second term: cos^2x - 2xsinx

  in xcos^2(x) derivitive? Comment by joni-danerd June 2021
• First use the product rule and you get x'cos^2x + x(cos^2x)' x' = 1, and apply the chain rule on the second term: cos^2x - 2xsinx

  in xcos^2(x) derivitive? Comment by joni-danerd June 2021
• First use the product rule and you get x'cos^2x + x(cos^2x)' x' = 1, and apply the chain rule on the second term: cos^2x - 2xsinx

  in xcos^2(x) derivitive? Comment by joni-danerd May 2021
• Not enough information. In addition to being differntiable on an open interval, f must also be continuous on a closed interval. Otherwise you can find counterexamples such as the one above. Given continity and differntiability, this follows from …

  in abstract math problem..? Comment by joni-danerd May 2021