F(x) = 7x^2 + 4, find and simplify using the derivative function f(a+h) -f(a)/ (h) ?
I'm not 100% sure what you are asking but I'm going to take a punt that you want to find the derivative of
Expanding out the squared bracket some terms helpfully cancel out:
Pleasingly this is what we would expect had we differentiated normally using the power rule.
We use the expression
#f'(x) =lim_(h->0) (7(x + h)^2 + 4 - (7x^2 + 4))/h#
#f'(x) = lim_(h->0) (7x^2 + 14xh + h^2 + 4 - 7x^2 - 4)/h#
#f'(x) = lim_(h->0) (14xh + h^2)/h#
#f'(x) = lim_(h->0) (h(14x + h))/h#
#f'(x) = lim_(h->0) 14x + h#
#f'(x) = 14x#
This matches what we would obtain using the power rule, where
Hopefully this helps!