• DА Zhunisbekova Республика Казахстан
  • NM Utenov Республика Казахстан
  • KhA Ashirbaev Республика Казахстан
  • AZh Suigenbaeva Республика Казахстан
  • AB Imanbaeva Республика Казахстан
  • A Saduakas Республика Казахстан


“Function’s study” is the most interesting theme of mathematical calculus. Let’s read it. First, let’s start with monotonicity. Finding the interval of functions’ monotonicity. The behavior of function is closely connected with the values of their derivatives, and, especially, with the sign of the first- and second-order derivatives. Theorem 1. If the differentiable function y=f(x) increases on an interval (a;b) then its derivative is positive f((x)>0. Theorem 2. If the function y=f(x) is continuous on the interval [a;b] and differentiable on this interval and f((x)>0, then the function y=f(x) increases on this interval. We can formulate the theorem for the decreasing function also: 1. If the function y=f(x) has the derivative on the interval (a;b) and is decreasing on it then its derivative is f((x)<0 on this interval.


1.Zhunisbekova D.A., Ashirbaev Kh.A. Higher Mathematics. - Shymkent: Publishing house “Alem”, 2018. – 360 p.



How to Cite

Zhunisbekova, D., Utenov, N., Ashirbaev, K., Suigenbaeva, A., Imanbaeva, A., & Saduakas, A. (2020). FUNCTION’S STUDY. Pridneprovskiy Scientific Bulletin, 11(667). Retrieved from