Question

Evaluate the function.
F(x)= X^3
f(x+(deltax))-f(x)/(deltax)
Please show step by step, or atleast how to set it up

Answer 1

Are you applying the product rule to get the 1st derivative or another one?

Answer 2

I think this could also be a limits problem. Please confirm the topic of the question

Answer 3

i think i have to evaluate the f(x)=x^3 into the second one. The answer is 3X^2 +3xdeltax +(deltax)^2 where deltax cannot equal zero. I am just not sure how to set it up

Answer 4

And it is just evaluating function at the given values. Not a limits problem

Answer 5

start by computing
\[f(x+h)=(x+h)^3\] i.e. multiply out

Answer 6

you know how to do this?

Answer 7

when i tried solving it like that i did not get the right answer... I just dont know the right set up

Answer 8

at the risk of repeating myself, the first step is to cube
\[(x+h)^3\]
do you know what you get? if not, i can show you, just asking

Answer 9

is this the first step for the set up?
\[f(x)= f(x+Deltax)^3 -x^3/ Deltax\]

Answer 10

ok lets go slow

Answer 11

no one wants to write \(\Delta x\) each time, so lets call it \(h\) which is very common

Answer 12

ok so f(x+h)^3 -x^3/h

Answer 13

you job it it to compute
\[\frac{f(x+h)-f(x)}{h}\] which has three parts, \(f(x+h), f(x)\) and \(h\)

Answer 14

after i am done cubing i get: hx^3 + 2hx^2+ 2h^2x^2 + h^2x^3 + h^3x^3/h

Answer 15

IS that correct or did i mess up cubing?

Answer 16

i think you might be confused about the notation
\[f(x)=x^3\] so for example
\[f(2)=2^3\] and
\[f(3)=3^3\] and
\[f(\pi)=\pi^3\]
notice it is not \(f(\pi)=f(\pi)^3\)

Answer 17

yeah you messed it up

Answer 18

how tho?

Answer 19

i am not sure what you did but
\[(x+h)^3=x^3+3x^2h+3xh^2+h^3\]

Answer 20

you can either do

\[(x+h)(x+h)(x+h)\] or else just know that
\[(a+b)^3=a^3+3a^2b+3ab^2+b^3\]

Answer 21

ok sorry i got it, i guess the delta x was throwing me off but i rewrote it with h and i got it now, thabk you sooo much

Answer 22

yw
the next job is to subtract \(f(x)=x^3\)
that will leave you with
\[3x^2h+3xh^2+h^3\] and your final job is to divide every thing by \(h\)

Answer 23

I got that one too satellite73 LOL...not as fast as you, at first thought I forgot something. Thanks for the calc refresher.

Answer 24

Do you mind answering another one based on that same concept but with radicals and fractions?

Answer 25

Satellite - after dividing by h; you have to go back and replace that with delta x, right?