- #1

- 35

- 0

## Homework Statement

Find the derivative from first principles, i.e, from the definition of f ' as a limit, for f(x)= [tex]\sqrt{}a-bx, where a and b are positive constants. What are the domains of f and f ' ?

## The Attempt at a Solution

I solved:

f(x) = \sqrt{a-bx} ---> f(x+h) = \sqrt{a-b(x+h)}

lim h-->0 = \sqrt{a-b(x+h)} - \sqrt{a-bx} / h

lim h-->0 = \sqrt{a-bx+bh-a+bx} / h

lim h-->0 = \sqrt{bh} / h

lim h-->0 = \sqrt{bh}* \sqrt{bh} / h\sqrt{bh}

lim h-->0 = b/ \sqrt{bh}

What did I do wrong here?

Please help and thanks

Last edited: