The Algebra of Functions

Question

The expression f(x+h)-f(x)/h for h ≠0 is called the difference quotient. Find and simplify the difference quotient for the following function. 

 

f(x)= -3x^2+9x+4

 

 

 

f(x+h)-f(x)/h means that f(x+h)-f(x) is all over h  

Answer 1

[f(x+h) - f(x)]/h = [-3(x+h)²+9(x+h)+4 - (-3x²+9x+4)]/h

 

                       = [-3(x²+2xh+h²)+9x+9h+4+3x²-9x-4]/h

 

                       = (-3x²-6xh-3h²+9x+9h+4+3x²-9x-4)/h

 

                       = (-6xh - 3h² + 9h)/h

 

                       = h(-6x - 3h + 9)/h

 

                       = -6x - 3h + 9