Final answer:
To find the unsimplified formula for fʹ(x), we need to take the limit as h approaches 0 of the expression (x+h)²-4(x+h)+5-(x²-4x+5)/h.
Step-by-step explanation:
To find the unsimplified formula for fʹ(x), we need to take the limit as h approaches 0 of the expression (x+h)²-4(x+h)+5-(x²-4x+5)/h.
We can start by expanding the squared term: (x+h)² = x²+2xh+h².
Plugging this back into the expression, we have: x²+2xh+h²-4(x+h)+5-(x²-4x+5)/h.
Next, we distribute the -4 to both terms inside the parentheses: x²+2xh+h²-4x-4h+5-(x²-4x+5)/h.
Combining like terms, we have: x²+2xh-4x-4h+h²+5-(x²-4x+5)/h.
Finally, we simplify by canceling out the x² terms: 2xh-4x-4h+h²+5-(4x-5)/h.
This is the unsimplified formula for fʹ(x).