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.😂😂