f(x+h)-f(x)/h f(x)=4x^2

Question

find and simplify the difference quotient x cannot equal zero for the function

Answer 1

f(x) = 4x²

 

[f(x+h) - f(x)]/h = [4(x+h)² - 4x²]/h

 

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

 

                       = [4x² + 8xh + 4h² - 4x²]/h

 

                       = [8xh + 4h²]/h

 

                       = [h(8x + 4h)]/h

 

                       = 8x + 4h

Answer 2

Step 1: Substitute (x + h) into f(x)

 

Step 2: Replace f(x + h) with the subsequent polynomial derived from substituting (x + h) into f(x); and replace f(x) with it's algebraic representation 4x^2

 

Step 3: Simplify the numerator of the given algebraic expression for f(x + h) - f(x)

 

Step 4: Then simplify the quotient expression by appropriately canceling the "h" from the denominator & numerator

 

Step 5: The resultant expression should be a monomial of degree "1" with all occurrences of "h" eliminated from the

            expression