Question

For the function g(x)=radical 5-x

Find the general formula for the instantaneous velocity using the definition of derivative

Answer 1

you want the limit as h->0 of

(√(5-(x+h)) - √(5-x))/h
= (√(5-(x+h)) - √(5-x))/h * (√(5-(x+h)) + √(5-x))/(√(5-(x+h)) + √(5-x))
= (5-(x+h))-(5-x))/(h(√(5-(x+h)) + √(5-x)))
= -h/h((√(5-(x+h)) + √(5-x)))
= -1/(√(5-(x+h)) + √(5-x))
now take the limit, and you get
-1/((√(5-x) + √(5-x))
= -1/(2√(5-x))