simplify the difference quotient

Question

f(x+h)-f(x)/h

 

for the given function  f(x)=19/x

Answer 1

Hi Hailey,

 

f(x+h) = 19/(x+h)

f(x) = 19/x

(x+h)-f(x) = 19/(x+h) - 19/x  (make the denominators equal by multiplying the first fraction by x and the second one by (x+h)

= (19x - 19(x+h)) / (x(x+h))

= (19x - 19x + 19h) / (x(x+h))

= (19h) / (x(x+h))

This is the result of the numerator of f(x+h)-f(x)/h

We need to divide it by h

= (19h) / (x(x+h)) / h (hs cancel out)

= 19 / (x(x+h))