Bonsoir,
f(x)=g(x)
[tex]\dfrac{x^2}{2} -\dfrac{3x}{2}+3=\dfrac{3x+13}{x+1}\\\\(x^2)-3x+6=6x+26\\\\x^3-2x^2-3x-20=0\\\\x^3-4x^2+2x^2-8x+5x-20=0\\\\x^2(x-4)+2x(x-4)+5(x-4)=0\\\\(x-4)(x^2+2x+5)=0\\\\x=4\ et\ f(4)=\dfrac{16}{2} -\dfrac{3*4}{2} +3=5\\\\f'(x)=x-\dfrac{3}{2} \Longrightarrow\ f'(4)=4-\dfrac{3}{2} =\dfrac{5}{2} \\\\g'(x)=\dfrac{3(x+1)-(3x+13)*1}{(x+1)^2} \Longrightarrow\ g'(4)= \dfrac{3*5-(12+13)}{5^2} =-\dfrac{2}{5} \\\\f'(4)*g'(4)=-1\\[/tex]
