SOLUTION: The difference quotient is defined to be {{{ (f(x+h)-f(x))/h }}}. Find the difference quotient for each of the following functions (make sure to reduce your answer). a. {{{ f(

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The difference quotient is defined to be {{{ (f(x+h)-f(x))/h }}}. Find the difference quotient for each of the following functions (make sure to reduce your answer). a. {{{ f(      Log On


   

Question 1046652: The difference quotient is defined to be +%28f%28x%2Bh%29-f%28x%29%29%2Fh+. Find the difference quotient for each of the following functions (make sure to reduce your answer).

a. +f%28x%29=x%2B1+
b. +f%28x%29=+x%5E2%2Bx+
c. +f%28x%29=x%5E3+
d. +f%28x%29=1%2Fx+
e. +f%28x%29=+sqrt%28x%29+
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a. +f%28x%29=x%2B1+
find +f%28x%2Bh%29
+f%28x%2Bh%29=%28x%2Bh%29%2B1
+f%28x%2Bh%29=x%2Bh%2B1
so,
+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28%28x%2Bh%2B1%29-%28x%2B1%29%29%2Fh

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28cross%28x%29%2Bh%2B1-cross%28x%29%2B1%29%2Fh

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28h%2B2%29%2Fh


b. +f%28x%29=+x%5E2%2Bx+

+f%28x%2Bh%29=%28x%2Bh%29%5E2%2B%28x%2Bh%29

+f%28x%2Bh%29=x%5E2%2B2xh%2Bh%5E2%2Bx%2Bh

+f%28x%2Bh%29=x%5E2%2B2xh%2Bh%5E2%2Bx%2Bh



+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28x%5E2%2B2xh%2Bh%5E2%2Bx%2Bh-x%5E2-x%29%2Fh



+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28h%5E2%2B2xh%2Bh%29%2Fh

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=cross%28h%29%28h%2B2x%2B1%29%2Fcross%28h%29

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=h%2B2x%2B1


c. +f%28x%29=x%5E3+

+f%28x%2Bh%29+=%28x%2Bh%29%5E3

+f%28x%2Bh%29+=h%5E3%2B3xh%5E2%2B3hx%5E2%2Bx%5E3

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28%28h%5E3%2B3xh%5E2%2B3hx%5E2%2Bx%5E3%29-x%5E3%29%2Fh



+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28h%5E3%2B3xh%5E2%2B3hx%5E2%29%2Fh

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=cross%28h%29%28h%5E2%2B3xh%2B3x%5E2%29%2Fcross%28h%29

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=h%5E2%2B3xh%2B3x%5E2


d. +f%28x%29=1%2Fx+

+f%28x%2Bh%29=1%2F%28x%2Bh%29

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%281%2F%28x%2Bh%29-1%2Fx%29%2Fh

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28x%2Fx%28x%2Bh%29-%28x%2Bh%29%2Fx%28x%2Bh%29%29%2Fh

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28x-%28x%2Bh%29%29%2F%28hx%28x%2Bh%29%29



+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=-1%2F%28x%28x%2Bh%29%29



e. +f%28x%29=+sqrt%28x%29+

+f%28x%2Bh%29=sqrt%28x%2Bh%29

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=%28sqrt%28x%2Bh%29-sqrt%28x%29%29%2Fh

+%28f%28x%2Bh%29-f%28x%29%29%2Fh+=sqrt%28x%2Bh%29%2Fh-sqrt%28x%29%2Fh