QuesLion find the difference quotient Given fx x 2 h 4 b x h

QuesLion find the difference quotient Given f(x) x 2 h 4 b) (x+ h 2) 2) (x +h 2)h d) (x +h+2)(x +2) h 0.

Solution

f(x) = 1/ ( x+ 2)

f(x+h) = 1 / {(x+h) + 2 }

plugging the values in difference quotient formula

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

= {1 / ( x+ 2) - 1 / ( x+ h+2 ) }/ h

( x+h+2 - x - 2 ) / h ( x+2)(x+h+2)

= 1 / ( x+2)(x+h+2)

(option b)