Question

given f(x) = 1/x, find f(1+Δx)-f(1) / (Δx)

Answer 1

i just need help on how to write the equation!

Answer 2

so i plug in 1/x inside of ever f( )

Answer 3

does that mean for the numerator i get ((1+Δx)/1) - (1/x) / Δx?

Answer 4

just replace
\[ \large \frac{f(1+\Delta x)-f(1)}{\Delta x}=
\frac{\frac{1}{1+\Delta x}-\frac{1}{1}}{\Delta x}= \]

Answer 5

hmmm. seems i did it wrong

Answer 6

we can call \(\Delta x\) \(h\) to make typing simpler and so you are looking for
\[\frac{\frac{1}{1+h}-\frac{1}{1}}{h}\]

Answer 7

no. it is the other way around: plug \(1+\Delta x\) into f(x)

Answer 8

your main work is this:
subtracting \[\frac{1}{1+h}-1\] that is the only hard part

Answer 9

yes. satellite73 is right.

Answer 10

you need \(1+h\) in the denominator, so compute via
\[\frac{1-(1+h)}{1+h}\] distribute carefully to get
\[\frac{-h}{1+h}\]

Answer 11

then (and only then) recall that you are dividing all this by \(h\) which gives
\[\frac{-1}{1+h}\]