Question

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

Answer 1

f'(x) = 8x +4h

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