CONVEXITIES, INFLECTION POINTS, AND ASYMPTOTES OF THE FUNCTION. FULL FUNCTION CHECK

Аннотация

Convexity, inflection points, and asymptotes of a function in this paper. The full function check is thought out and explained with examples. Keywords:function, skewness, point, derivative, graph. Supposethat thefunction isgiven by,and let be for . a straig h(t )line passing( t,h r)ough the points 1, 2o∈f( th,e )gra ph1 ly c(o n)vex)function. concave and convex functions are depicted in Figure 1: http://www.internationaljournal.co.in/index.php/jasass 347 Volume15 Issue02, February2025 Impact factor: 2019: 4.679 2020: 5.015 2021: 5.436, 2022: 5.242, 2023: 6.995, 2024 7.75 Drawing 1. Let's say, be and be. The concave andconvexity of a function can also bedefined as follows. 1 ≥ 0, 2 ≥ 0, 1 + 1 = 1 х∀ 1х, 2 ∈а( , ) Definition3.If ( 1. 1 + 2 2) ≤ 1 1( 1)+ 2 ( 2) If , thefunction is sa(i d1t. o1b+ec o2n c2a)v (s tr1ic t(ly 1c)o+nv ex2) .( 2) Exa m( p)le1.This​ ​ ( , ) 2 Thefunction is Ralso a strictlyconcave fun c(t io)n=. Solution.Using Definition 3,we find: 2 2 2 ( 1 1 + 2 2) = ( 1 1 + 2 2) = ( 1 1) +2 1 2 1 2 +( 2 2) 0) Forthis function ″ 1 AccordingtoTheorem 2,the given f (x ) (= ) ln = x fu n 2 c 0 http://www.internationaljournal.co.in/index.php/jasass 350 Volume15 Issue02, February2025 Impact factor: 2019: 4.679 2020: 5.015 2021: 5.436, 2022: 5.242, 2023: 6.995, 2024 7.75 Definition 5. If a function is concave (convex) a