If f(x) = 2x2 – x + 5 and h ≠ 0, find the following and simplify.

Question

(a)    f(x + h)          =

(b)     (f(x + h) – f(x) h)/h =

Answer 1

f(x) = 2x^2 -x +5 and h does not = zero

find f(x+h) = 2(x+h)^2 - x -h +5= 2x^2 +4xh + 2h^2 -x -h +5

find (f(x+h) - f(x))/h = (4xh - h +2h^2)/h = 4x-1 +2h

it's the same as f"(x) but with an h term added in

that's the purpose of this problem, to introduce you to differential calculus where he goes to zero as a limit

odds are you copied the problem wrong, with a typo or maybe a mis print

you have an extra h

as you ask to find (f(x+h) - f(x)h)/h

you should have just (f(x+h) - f(x))/h

as written, the answer is f(x+h)/h - f(x) which has no relevance to differential calculus

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

= 2x^2/h +4x +h -x/h -1 +5/h -2x^2 -x +5

= 2x^2/h +3x +h -x/h +4 +5/h,

a relatively meaningless expression

Answer 2

I think you do this by substitution of "x+h" wherever you have an x in the original f(x) function for question a.

 

And so on for question b.