Question

someone please explain this to me.

Answer 1

For the given function f(x), write a formula for \[\frac{ f(x+h)-f(x) }{ h }\]and if possible simplify

\[f(x)=x^2-2x+3\]

Answer 2

f(x+h)=(x+h)^2-2(x+h)+3
f(x+h)=x2+h2+2xh-2x-2h+3
so

f(x+h)-f(x)=x2+h2+2xh-2x-2h+3-x2+2x-3
f(x+h)-f(x)=h2+2xh-2h
f(x+h)-f(x)=h(h+2x-2)
f(x+h)-f(x)/h=h(h+2x-2)/h
f(x+h)-f(x)/h=h+2x-2

Answer 3

now if h->0 then

f(x)=2x-2

which shows that it is exactly the derivative of above function..

and also the above given formua is gen.def.of derivative of any functio.n.

Answer 4

wow...great. thanks!

Answer 5

yw @Mokeira