Question

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

Answer 1

`=-4`.

Explanation:

The Derivative of a function `f : f(x)=-4x+2,` at `x` is denoted

by `f'(x),` and, is defined by,

`f'(x)=lim_(trarrx)(f(t)-f(x))/(t-x)`.

`:. f'(x)=lim_(trarrx) {(-4t+2)-(-4x+2)}/(t-x)`

`=lim_(trarrx) -4cancel((t-x))/cancel((t-x)`

`=lim_(trarrx) -4`

`=-4`.