Bonsoir,
[tex]f(x)=x^2\\
f(2+h)=(2+h)^2\\
f(2)=2^2\\
\dfrac{f(2+h)-f(2)}{h} =\dfrac{(2+h-2)(2+h+2)}{h}\\\\
=\dfrac{h(h+4)}{h}=h+4\\\\
f'(2)= \lim_{h \to 0}(h+4)=4\\\\
[/tex]
[tex]f(x)=x^2-x\\
f(1+h)=(1+h)^2-(1+h)=(1+h)(1+h-1)=(1+h)h\\
f(1)=1^2-1=0\\
\dfrac{f(1+h)-f(1)}{h} =\dfrac{(1+h)h-0)}{h}\\\\ =h+1\\\\
f'(1)= \lim_{h \to 0}(h+1)=1\\\\[/tex]
