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
Explanation:
The definition of the derivative of
f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h
So Let
f(x+h) = -2(x+h) + 4
" "= -2x-2h + 4
And so
f(x+h)-f(x) = (-2x-2h + 4 ) - (-2x+4)
" "= -2x-2h + 4 +2x-4
" "= -2h
And so the derivative of
\ \ \ \ \ dy/dx = lim_(h rarr 0) (-2h) / h
" " = lim_(h rarr 0) -2
" " = -2
:. dy/dx = -2