Evaluate, f (x) = 4x^2+1 given f (x) = f (x+h) - f (x) / h

f' (x) = 8x + 4h

Step-by-step explanation:

For f (x) = 4x^2 + 1, we have ...

f (x+h) = 4 (x + h) ^2 + 1 = 4x^2 + 8xh + 4h^2 + 1

Then ...

f' (x) = (f (x+h) - f (x)) / h = ((4x^2 + 8xh + 4h^2 + 1) - (4x^2 + 1)) / h

= (8xh + 4h^2) / h

f' (x) = 8x + 4h