Difference Quotient

Question

Let f(x) = 4 + 7 x -x^2. Find the difference quotient f(5+h)-f(5)/h. Simplify your answer.

Answer 1

 

f(5 + h) = 4 + 7(5 + h) - (5 + h)^2

 

           = 4 + 35 + 7h - ( 25  + 10h +  h^2)

 

           = 39 + 7h - 25 - 10h - h^2

 

          = 14 - 3h - h^2

 

 

 

f(5) = 4 + 7*5 - 5^2 = 4 + 35 - 25 = 39-25 = 14

 

f(5+h)-f(5) = -h^2 - 3h

 

Dividing that by h results in -h - 3