f(x)=2x^2+1 and g(x)=3x-2
find f(x+h)-f(x)
To find f(x+h) - f(x), we need to substitute f(x+h) and f(x) into the expression and then simplify.
First, let's find f(x+h):
Replace x in f(x) with (x+h):
f(x+h) = 2(x+h)^2 + 1
Expand and simplify:
f(x+h) = 2(x^2 + 2xh + h^2) + 1
= 2x^2 + 4xh + 2h^2 + 1
Next, let's find f(x):
Replace x in f(x) with just x:
f(x) = 2x^2 + 1
Now, substitute f(x+h) and f(x) into the expression f(x+h) - f(x):
f(x+h) - f(x) = (2x^2 + 4xh + 2h^2 + 1) - (2x^2 + 1)
Simplify by removing the parentheses:
f(x+h) - f(x) = 2x^2 + 4xh + 2h^2 + 1 - 2x^2 - 1
Combine like terms:
f(x+h) - f(x) = 4xh + 2h^2
Therefore, f(x+h) - f(x) = 4xh + 2h^2.