I am not sure what to do here:

Question

Find the derivative (f '(x) using the limit process

a). f(x)= 2x^2+5x+2 find f ' (2)

b.) Find the equation of the Tangent Line at (1,5)

Answer 1

suppressing the limit notation for the moment,

f' = [f(x+h)-f(x)]/h
f' = [(2(x+h)^2 + 5(x+h) + 2) - (2x^2 + 5x + 2)]/h
f' = [(2x^2 + 4xh + 2h^2) + (5x + 5h) + 2 - (2x^2 + 5x + 2)]/h
f' = (4xh + 2h^2 + 5h)/h
f' = 4x + 5 + 2h
lim as h->0 = 4x+5
-------------------------
f'(1) = 9

(y-5) = 9(x-1)

Answer 2

Thank you so so much! I finally understand what to do! :)