Hints, tips, or advice for evaluating this limit?

f(x) = 2x^2 - 3x - 5





(a) Show that the slope of the secant line through (2, f(2)) and (2 + h, f(2 + h)) is 2h + 5.





(b) Use the formula in (a) to compute the slope of the secant line through (2, f(2)) and (3, f(3)).





(c) Use the formula in (a) to compute the slope of the tangent line at x = 2 (by taking a limit).





I understand partly how this is done - I'm supposed to use either the definition of the derivative or the definition of the tangent line, right? You don't need to solve everything, but at least help point me in the right direction so I can solve these and all the others i've got? It would be a big help! I'll give 10 points to the most helpful answer!Hints, tips, or advice for evaluating this limit?
First find an expression for f(2+h) by substituting 2+h for x in your defining formula. This gives


f(2+h)=2(2+h)^2 - 3(2+h) - 5


= (8 + 8h + 2h^2) - (6+3h) - 5


= -3 + 5h + 2h^2


This also gives f(2) = f(2+0) = -3.





By definition, the slope of the secant line through


(2, f(2)) and (2+h, f(2+h)) will be





(f(2+h) - f(2))/((2+h) - 2) = ( -3 + 5h + 2h^2 - (-3))/h


= 5 + 2h


This solves a.





b. can be solved by substituting into the formula from a. In c., you take a limit of the formula from a.