Find (f(x+h)-f(x))/h for the 3x2+3

Question

Using the f(x) = 3x²+3 find (f(x+h)-f(x))/h

Answer 1

In general, if you plug in something other than x into f(x) then replace all x's in the definition by this new quantity. For example,

f(x) = x^2 therefore f(x+1) = (x+1)^2 = x^2 +2 x + 1 or

f(x) = 2 x - 1 therefore f( x + h ) = 2(x+h) - 1 = 2 x + 2 h - 1

Note the use of parentheses. This avoids errors relating to negative signs.

Now follow the same procedure as above for your given function. Treat h as just a number like I did above in the second example.