Question

Find derivative of 3x^2+4 using limits

Answer 1

The derivative of a function f(x) is defined as

`f'(x)=\displaystyle\lim_(h\to0)\frac{f(x+h)-f(x)}h`

For f(x) = 3x ² + 4, we have

`f'(x)=\displaystyle\lim_(h\to0)\frac{(3(x+h)^2+4) - (3x^2+4)}h`

`f'(x)=\displaystyle\lim_(h\to0)\frac{(3(x^2+2xh+h^2) - 3x^2}h`

`f'(x)=\displaystyle\lim_(h\to0)\frac{6xh+3h^2}h`

`f'(x)=\displaystyle\lim_(h\to0)(6x+3h) = \boxed{6x}`