Question

How do you use the limit definition to find the derivative of `y=-4x-5`?

Answer 1

`dy/dx = -4`

Explanation:

By definition `f'(x) =lim_(hrarr0)( (f(x+h)-f(x))/h )`

So, with `y=-4x-5` we have:
`dy/dx = lim_(hrarr0)( ( (-4(x+h)-5) - (-4x-5) ) / h )`
`:. dy/dx = lim_(hrarr0)( ( (-4x-4h-5) - (-4x-5) ) / h )`
`:. dy/dx = lim_(hrarr0)( ( -4x-4h-5 +4x+5 ) / h )`
`:. dy/dx = lim_(hrarr0)( -(4h) / h )`
`:. dy/dx = lim_(hrarr0)( -4 )`
`:. dy/dx = -4`