Homework Soursegiven fx2x3 find the difference quotient fxhfxh h can not e
given f(x)=2/(x+3)
find the difference quotient f(x+h)-f(x)/h , h can not equal 0
Solution
given
f(x)=2/(x+3)
f(x+h)=2/((x+h)+3)
f(x+h)=2/(x+h+3)
f(x+h)- f(x)=[2/(x+h+3) -2/(x+3)]
f(x+h)- f(x)=2[(x+3)-(x+h+3)]/((x+h+3)(x+3))
f(x+h)- f(x)=2[-h]/((x+h+3)(x+3))
f(x+h)- f(x)= -2h/((x+h+3)(x+3))
divide by h on both sides
[f(x+h)- f(x)]/h= [-2h/((x+h+3)(x+3))]/h
[f(x+h)- f(x)]/h= -2/((x+h+3)(x+3))
difference quotient f(x+h)-f(x)/h = -2/((x+h+3)(x+3))
