How do you use the limit definition of the derivative to find the derivative of f(x)=4x^2+1?

1 Answer
Steve M
Oct 24, 2016

f'(x) =8x

Explanation:

By definition f'(x) =lim_(hrarr0)(f(x+h)-f(x))/h

So, with f(x)=4x^2+1 we have:

f'(x) =lim_(hrarr0) ((4(x+h)^2+1 ) - (4x^2+1) ) / h
:. f'(x) =lim_(hrarr0) ((4(x^2+2hx+h^2)+1 ) - 4x^2-1 ) / h
:. f'(x) =lim_(hrarr0) (4x^2+8hx+4h^2+1 - 4x^2-1 ) / h
:. f'(x) =lim_(hrarr0) (8hx+4h^2) / h
:. f'(x) =lim_(hrarr0) (8x+4h)
:. f'(x) =8x

Related questions
See all questions in Limit Definition of Derivative
Impact of this question
1411 views around the world
You can reuse this answer
Creative Commons License