Using the limit definition, how do you find the derivative of # f(x)=4x^2#?
1 Answer
May 2, 2016
Explanation:
The limit definition of a derivative states that
#f'(x)=lim_(hrarr0)(f(x+h)-f(x))/h#
Substituting
#f'(x)=lim_(hrarr0)(4(x+h)^2-4x^2)/h#
From this point on, you want to expand and simplify.
#f'(x)=lim_(hrarr0)(4(x^2+2xh+h^2)-4x^2)/h#
#f'(x)=lim_(hrarr0)(4x^2+8xh+4h^2-4x^2)/h#
#f'(x)=lim_(hrarr0)(h(8x+4h))/h#
#f'(x)=lim_(hrarr0)8x+4h#
Plugging in
#f'(x)=8x+4(0)#
#color(green)(|bar(ul(color(white)(a/a)color(black)(f'(x)=8x)color(white)(a/a)|)))#