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Find the difference quotient of​ f' that​ is, find [f(x + h) - f (x)]/h, h is not equals 0, for the following function. Be sure to simplify.

f(x)= 2x^2 - x + 3

Answer :

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]

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