F(x+h)-F(x)/h?

Question

For the function F(X)= 2x squard-x+5 write and simplify the expression using: F(x+h)-F(x)/h

Answer 1

do you want to find the limit of this too?

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

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

so, f(x+h) - f(x) =

2(x+h)^2 - (x+h) + 5 - (2x^2 - x + 5) =

2(x^2 + 2hx + h^2) - x - h + 5 - 2x^2 + x - 5 =

4hx + 2h^2 - h + 2x^2 - 2x^2 - x + x + 5 - 5 =

4hx + 2h^2 - h =

h(4x + 2h - 1)

So, divide that by h to get (4x + 2h - 1) = f(x+h)-f(x) / h

(Note that the limit of this as h approaches 0 is 4x-1)

~ dualspace ~

Answer 2

((2(x+h)² - (x+h) + 5) - (2x² - x + 5))/h

= (2x² + 4xh + 2h² - x - h + 5 - 2x² + x - 5)/h

= (4xh + 2h² - h)/h

= h(4x + 2h - 1)/h

= 4x + 2h - 1

If you needed to find the limit of this expression as h approaches 0, it would further simplify to:

4x - 1



*** The guy above me is wrong. It's "- 1," not "+ 1."

Answer 3

f(x)=2x^2-5+5
f(x+h)=2(x+h)^2-(x+h)+5
(f(x+h)-f(x))/h=(2((x+h)^2-x^2)-((x+h)-x)+5-5)/h
(f(x+h)-f(x))/h=(2(2xh+h^2)-h)/h=(4xh+h^2-h)/h=4x+h-1
this is, of course how to find deriviatives. in the limit h---->0 this becomes 4x-1 which is f'(x).