For f(x) = 2x^2 - 3x, find and simplify f(2+h)-f(2)?

Answer 1

By having f(?) that ? replaces the x in your original equation. Therefore, if we take our fucntion f(x) = 2x^2 - 3x and apply f(2+h) - f(2) we get

2(2+h)^2 - 3(2+h) - 2(2)^2 - 3(2) and now we want to simplify so lets first do the exponents

2(4 + 4h + h^2) - 3(2+h) - 2(4) - 3(2) now distribute into the ( )

8 + 8h + 2h^2 - 6 - 3h -8 - 6 and now combine like terms

2h^2 + 5h -12 and if you want to further simplify, you factor into

(2h - 3)(h + 4)

and so your answer f(2+h) - f(2) = (2h - 3)(h + 4)

Answer 2

f(x) = 2x^2 - 3x

f(2 + h) means simply substitute 2+h in place of x

f(2+h) = 2(2+h)^2 -3(2 + h) =

2[4 + h^2 + 4h] - 6 - 3h =
8 + 2h^2 + 8h - 6 -3h =
2h^2 + 5h + 2

f(2) =2(2)^2 - 3(2) =
= 2(4) - 6 =
= 8 - 6 = 2

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

This is nothing but derivative of f(x),
when x tends to 2, h =(x - 2) tends to zero

Answer 3

2x^2 - 3x = x (2x - 3)

solutions are what x=1 1/2 and x =0

I wish you had stated this was a composite function