Question Number 100388 by Ar Brandon last updated on 26/Jun/20

       Given f:[0,2]→R , f(x) is twice derivable and   f(0)=f(1)=f(2)=0  i-Show that there exist c_1 , c_2 , such that f′(c_1 )=0   and f′(c_2 )=0  ii-Show that there exist c_3  such that f′′(c_3 )=0

Answered by maths mind last updated on 26/Jun/20

f(0)=f(1)⇒∃c∈]0,1[,  f′(c_1 )=0  f(1)=f(2)⇒∃c_2 ∈]1,2[ f′(c_2 )=0  let f′(x) over [c_1 ,c_2 ]   f′(c_1 )=f′(c_2 )⇒∃c_3 ∈[c_1 ,c_2 ]such f′′(c_3 )=0  i used if f continus differentiabl over [a,b] such  f(a)=f(b)⇒∃c∈[a,b] such f′(c)=0.Roll theorem

Commented byDGmichael last updated on 26/Jun/20

👍very good.

Commented byAr Brandon last updated on 26/Jun/20

Thanks 💞

Commented byAr Brandon last updated on 26/Jun/20

Ouaye DG, dès que ce monsieur se connecte oulala !😅 On dirait une machine qui venait d'être activée.😂😂