The difference quotient of the function f(x) = 4x + 2 is 4.
Functions were originally the idealization of how a varying quantity depends on another quantity.
The given function is,
f(x) = 4x + 2
For a given function f(x), we define the difference quotient as:
[tex]\frac{f(x+ h)-f(x)}{h}[/tex]
Thus, for the given function, difference quotient is given as,
[tex]\frac{f(x+ h)-f(x)}{h}[/tex] = [tex]\frac{4(x+h)+2-(4x+2)}{h}[/tex]
expanding the brackets we get,
[tex]\frac{f(x+ h)-f(x)}{h}[/tex] = [tex]\frac{4x+4h+2-4x-2}{h}[/tex]
Solving we get,
⇒ [tex]\frac{f(x+ h)-f(x)}{h}[/tex] = [tex]\frac{4h}{h}[/tex]
Thus,we get
⇒ [tex]\frac{f(x+ h)-f(x)}{h}[/tex] = 4
Thus, the difference quotient of the function f(x) = 4x + 2 is 4.
To learn more about difference quotient :
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