Question

If f(x) = 4x^2 -3x+1, find (f(x+h)-f(x))/(h))

Answer 1

For f(x+h), replace all x by x+h in 4x^3 -3x+1.
For f(x), it's just 4x^3 -3x+1.
\[ \frac{f(x+h)-f(x)}{h} = \frac{(4(x+h)^3 -3(x+h)+1) - (4x^3 -3x+1)}{h} =...\]

Answer 2

Since this is how you get the derivative for small h,
you should find answer close to 12x^2 - 3.

Answer 3

okay I wrote the wrong equation b4, but I just corrected it. What is the next step after I write out: (4(x+h)^2 -3(x+h)+1)-(4x^2 -3x+1)/h)