Bonjour ZekiaChin
Exercice 1
f(x) = -7x² + 4x - 9
f '(x) = -14x + 4
[tex]\begin{array}{|c|ccc|} x&-\infty&&\frac{2}{7}\\&&&\\f'(x)&&+&\\&&&\\f(x)&&\nearrow&\\ \end{array}[/tex]
Exercice 2
[tex]f(x)=\dfrac{-3+10x}{4+7x}\\\\\\f'(x)=\dfrac{(-3+10x)'(4+7x)-(-3+10x)(4+7x)'}{(4+7x)^2}\\\\\\f'(x)=\dfrac{10\times(4+7x)-(-3+10x)\times7}{(4+7x)^2}\\\\\\f'(x)=\dfrac{40+70x+21-70x}{(4+7x)^2}\\\\\\\boxed{f'(x)=\dfrac{61}{(4+7x)^2}}[/tex]
Exercice 3
[tex]f(x)=(-3x-8)(-2x-9)\\\\f'(x)=(-3x-8)'(-2x-9)+(-3x-8)(-2x-9)'\\\\f'(x)=(-3)\times(-2x-9)+(-3x-8)\times(-2)\\\\f'(x)=6x+27+6x+16\\\\\boxed{f'(x)=12x+43}\\\\\\\\\begin{array}{|c|ccc|} x&-\frac{43}{12}&&+\infty\\&&&\\f'(x)&&+&\\&&&\\f(x)&&\nearrow& \end{array}[/tex]
Exercice 4
[tex]\begin{array}{|c|ccc|} x&-4&&3\\&&&\\f(x)&-8&\nearrow&0 \end{array}[/tex]
