حل تمرين 61الصفحة64 لكتاب الرياضيات من فضلكم

[black_host]

salam 3alicom li hal moukhtasser wa lakin tabi3 ma3i rah tefhame
wa a3ttathir 3ala 3adem tawafour el logha arabia
1- f(1)=2
-f'(1)=
y=f'(x').(x-x') + f(1) x'=1
=> y=f'(1).(x-1) + f(1)
wa bi akheth el no9ta a(16/9 ; 1/2)
==> 1/2=f'(1)(16/9-1)+2
ba3da el hisabe
f'(1)=27/14
2-
f(x)>0 ==> [1/4;3.75]
f'(x)>0 win takoudala moutazaida takoune el moushta9a +
[0;7/4]
f(x)<1 [0;1/2]u[13/4;5]
3- f(x)=a+bx(2-xpuissance1/2)==> ba3da el ishti9a9E nadjede f'(x)=b(2-3/2xpuissance 1/2)
4-f'(1)=27/14
wa f'(1)=b(2-3/2) ba3da el hissabe najed b=27/7
wa fi ta3wid fi f(x)
najede a =-13/7
inchaalah rah ykoune mafhoume