Answer: The difference quotient of f' is [tex]2h-4x-1[/tex]
Step-by-step explanation:
Since we have given that
[tex]\dfrac{f(x+h)-f(x)}{h}[/tex]
Here, [tex]f(x)=2x^2-x+3[/tex]
So,
[tex]f(x+h)=2(x+h)^2-(x+h)+3=2(x^2+h^2+2xh)-x-h+3=2x^2+2h^2+4xh-x-h+3[/tex]
So, we put in the given expression,
[tex]\dfrac{2x^2+2h^2+4xh-x-h+3-2x^2+x-3}{h}\\\\=\dfrac{2h^2-4xh-h}{h}\\\\=2h-4x-1[/tex]
Hence, the difference quotient of f' is [tex]2h-4x-1[/tex]
