Question

find the derivative of x^3+4x-2 using the def. of a derivative

Answer 1

3x^2+4

Answer 2

the definition of a derivative is lim h->0 [f(x+h) - f(x)]/h

Answer 3

so let f(x) = x^3 + 4x - 2
and plug in x+h
then plug in x
into the function and solve for the limit.
Through expansion and simlification, the h in the denominator should cancel with a factored h from the numerator and the result is the derivative