Use the definition of the derivative to find f'(x)

Question

1. f(x) 2x^2 + x - 1

Before the final step, my 'result' looked weird and I think I did something wrong in my arithmetic...someone correct me?

Here's my work...

BEGINNING STEP:
lim [2(x + deltaX)^2 - (x + deltaX) - (2x^2 + x - 1)] / deltaX

near the end step:
lim [4x + 2deltaX - 2x^2 - 1] / deltaX

Thanks

Answer 1

You started correctly, but you must have a math error in the intermediate steps.

((2(x+deltaX)^2 + (x+deltaX) - 1) - (2x^2 + x - 1) )/deltaX
=((2x2+4(x*deltaX) + 2deltaX^2 + x + deltaX - 1) - (2x^2 + x - 1) ) /deltaX
=(4(x*deltaX) + 2*deltaX^2 + deltaX)/deltaX
=4x + deltaX + 1
limit as delatX goes to 0
=4x + 1

Answer 2

Ooops!
the step before the limit statement should have read:
4x + 2deltaX + 1