Answer:
6x
Step-by-step explanation:
Given that a function f(x) is given as
[tex]y=f(x) = 3x^2[/tex]
A) [tex]f(x+ \Delta x) = 3((x+ \Delta x)^2=3(x^2+2x \Delta x+\Delta x^2)\\f(x) = 3x^2\\f(x+ \Delta x) -f(x) = 6x \Delta x +\Delta x^2[/tex]
Now divide by delta x
[tex]\frac{f(x+ \Delta x) -f(x)}{\Delta x}\\=6x+\Delta x[/tex]
B) When delta x tends to 0, this becomes
[tex]6x[/tex]
(NOte: This is the derivative of f(x))
