For each of the following functions determine (f(x+h)-f(x)) / h and express your answer in simple form.

a) f(x)= sqrt(3+4x)

Question

For each of the following functions determine (f(x+h)-f(x)) / h  and express your answer in simple form.

a) f(x)= sqrt(3+4x)

baldymcgee6 · Answer

@ganeshie8

baldymcgee6 · Answer

first principles? ish?

ganeshie8 · Answer

yea but its not exactly, theres no limit thingy :P

 put the expression and try to rationalize numerator. i see h would get cancel out may be

baldymcgee6 · Answer

I don't know how to setup the expression

ganeshie8 · Answer

okay!

f(x) is already given.

to setup the expression, we need f(x+h) right ?

ganeshie8 · Answer

$f(x) = \sqrt{3+4x}$

$f(x+h) = \sqrt{3+4(x+h)}$

baldymcgee6 · Answer

okay right, thank you.. i should get it from here

ganeshie8 · Answer

i just replaced x with (x+h)

ganeshie8 · Answer

oh great ! put the expression and rationalize numerator. h in the bottom cancels... . good luck :)

anonymous · Answer

After rationalizing you should obtain
$$
\frac{4}{\sqrt{4 (h+x)+3}+\sqrt{4 x+3}}
$$

anonymous · Answer

If h goes to zero, you get
$$
\frac{2}{\sqrt{4 x+3}}
$$
Which is the derivative f(x)