If f(x) = x^2 - 2x what does ( f ( x + h ) - f ( x ) ) / h simplified to?

Question

please help. i cannot figure out how to do this problem

Answer 1

Do the problem as you would any other function problem

((x+h)^2-2(x+h))-x^2+2x)/h

answer: 2x-2+h

Answer 2

That's asking for the derivative of f(x)

Simple answer is : 2x - 2

Using ( f ( x + h ) - f ( x ) ) / h method.

lim h ->0 [(x+h)^2 - 2(x+h) - x^2 + 2x]/h

lim h ->0  [x^2+h^2+ 2xh - 2x -2h -x^2 +2x]/h

lim h ->0 [h^2 + 2xh-2h]/h

lim h ->0  [h + 2x -2]

Giving 2x -2

Answer 3

[ (x+h)² - 2(x+h) - (x² - 2x) ] / h

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

= [ 2xh + h² - 2h ] / h

= 2x + h - 2

hope that helped :)

Answer 4

f (x + h) = (x + h)² - 2(x + h)

f (x + h) = x² + 2 h x + h² - 2x - 2h

f (x + h) = x² + 2 h x + h² - 2x - 2h

f (x) = x² - 2x

f(x + h) - f (x) = 2hx + h² - 2h

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

f `(x) = 2x - 2