Question

What is the limit definition of f'(x) and use it to find f'(x) for f (x) 5x^2 - 2

Answer 1

[f(x+h)-f(x)]/h as h-->0

if f(x) = 5 x^2-2
then
f(x+h) = 5(x+h)^2 - 2
5 x^2 + 10 xh + h^2 -2
-5 x^2 -2

= 10 xh +h^2
divide by h
= 10 x + h
take limit as h-->0
= 10 x
done