Find f '(x) using the diff. quotient for f(x) = 2x^2 + 3x
After I worked it, I got 4x + 5h, but I want confirmation. 10 points for steps.
After I worked it, I got 4x + 5h, but I want confirmation. 10 points for steps.

You're missing something.
f(x + h) = 2(x+h)² + 3(x + h) = 2x² + 4xh +2 h² + 3x + 3h
so
f(x + h)  f(x) = 4xh + 2h² + 3h
For h different from zero
[f(x + h)  f(x)]/h = 4x + 2h + 3.
f(x + h) = 2(x+h)² + 3(x + h) = 2x² + 4xh +2 h² + 3x + 3h
so
f(x + h)  f(x) = 4xh + 2h² + 3h
For h different from zero
[f(x + h)  f(x)]/h = 4x + 2h + 3.