If f(x) = x2, find the value of  
f(x + r) - f(x)
r
 .


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Answer:

2x + r

Step by Step Explanation:
  1. According to the question, f(x) = x2.
    Or, f(x + r) = (x + r)2
  2. Now,  
    f(x + r) - f(x)
    r
      =  
    (x + r)2 - x2
    r
     
    =  
    x2 + r2 + 2xr - x2
    r
     
    =  
    r2 + 2xr
    r
     
    =  
    r(r + 2x)
    r
     
    = r + 2x
    = 2x + r
  3. Therefore, the value of  
    f(x + r) - f(x)
    r
      is 2x + r.

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