Final answer:
To find the derivative of the function using the definition of derivative, apply the limit definition of derivative and simplify the expression.
Step-by-step explanation:
To find the derivative of the given function using the definition of derivative, we first need to apply the limit definition of derivative.
The limit definition of derivative states that the derivative of a function f(x) is equal to the limit of the difference quotient as the change in x approaches zero.
Let's apply this definition to the given function:
f(x) = 4 - 8x + 8x²
f'(x) = lim┬(h->0)〖(f(x+h)-f(x))/h〗
Now we can substitute the function into the definition and simplify:
f'(x) = lim┬(h->0)((4-8(x+h)+8(x+h)²)-(4-8x+8x²))/h
f'(x) = lim┬(h->0)(4-8x-8h+8x²+16xh+8h²-4+8x-8x²)/h
f'(x) = lim┬(h->0)(8h+8h²)/h
f'(x) = lim┬(h->0)8+8h = 8
Therefore, the derivative of the function f(x) = 4 - 8x + 8x² using the definition of derivative is 8.