How do you use the limit definition of the derivative to find the derivative of y=-2x+5y=2x+5?

1 Answer
Jan 1, 2017

dy/dx = -2 dydx=2

Explanation:

The definition of the derivative of y=f(x)y=f(x) is

f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h

So Let f(x) = -2x+5 then;

f(x+h) = -2(x+h) + 4
" "= -2x-2h + 4

And so f(x+h)-f(x) is given by:

f(x+h)-f(x) = (-2x-2h + 4 ) - (-2x+4)
" "= -2x-2h + 4 +2x-4
" "= -2h

And so the derivative of y=f(x) is given by:

\ \ \ \ \ dy/dx = lim_(h rarr 0) (-2h) / h
" " = lim_(h rarr 0) -2
" " = -2
:. dy/dx = -2