fx 4x 4 find the difference quotient fx h fxh h notequal

f(x) = 4/x + 4 find the difference quotient f(x + h) - f(x)/h, h notequalto 0

Solution

f(x) = x/(x+4)

f(x+h) (x+h)/(x+h+4)

f(x+h) - f(x) = (x+h)/(x+h+4) -x/(x+4)

= ((x+h)(x+4) -x(x+h+4))/x(x+h+4)

= [ x^2 +4x+ hx+4h -x^2 -xh -4x)/x(x+h+4)

= 4h/x(x+h+4)

Now differenc quotient [ f(x+h) -f(x)]/h

= 4h/x(x+h+4)/h

= 4/x(x+h+4)

So, difference quotient