Difference Quotient

Question

If f(x)=6+x+x² and h does not equal zero,

find f(x+h)-f(x)/h

Thank you for any help!

Answer 1

f(x) = x² + x + 6

[f(x+h) - f(x)] / h = [(x+h)² + (x+h) + 6 - (x² + x + 6) ] / h

= [x² + 2xh + h² + x + h + 6 - x² - x - 6] / h

= (2xh + h² + h} / h

= h(2x + h + 1) / h = 2x + h + 1