Functions and quotients

Question

Suppose f(x) = 5x² + 7x - 4. Assuming h doesn't equal 0 compute and simplify the difference quotient: f(x+h)-f(x) / h

 

Answer 1

[f(x+h) - f(x)]/h = [5(x+h)²+7(x+h)-4 - (5x²+7x-4)]/h

 

                       = [5(x²+2xh+h²)+7x+7h-4-5x²-7x+4]/h

 

                       = [5x²+10xh+5h²+7x+7h-4-5x²-7x+4]/h

 

                       = [10xh+5h²+7h]/h

 

                       = h(10x+5h+7)/h = 10x + 5h + 7