Question

Sub 3 BAC———————————————

Answer 1

Răspuns:

Explicație pas cu pas:

f'(x) =2020x^2019

f"(x) =2020*2019x^2018

prsupunenm ca

f(n) (x) =2020*2019*(2020-n+1)x6(2020-n)

o demonstrzi prin inductie, sorry, iti las tie placerea asta

f(2020) (x) =2020!x^0=2020!

b) y-f(1) =f'(1) (x-1)

f(1)=1^2020+1=1+1=2

f'(1) =2020*1^2019=2020

y-1=2020(x-1)

y=2020x-2020+1

y=2020x-2019

f"(x) =f"(x) =2020*2019x^2018 ≥0 , ∀∈R, deci convezaxa pe R

Obs pt x=0 f"(x)=0, dar nu schimba semnul in vecinatatea lui 0, deci nu schimba convexitatea