Let f(x) be the function 1/(x+9). Then the quotient [f(5+h)−f(5)]/h can be simplified to −1/(ah+b). What...?
does a and b equal to?
So I understand the overall concept, and did f(5+h) = 1/(14+h) and f(5) = 1/14.
Then to subtract the two, you get the common denominator which is 14(14+h).
So when you subtract it becomes (14-14+h)/[14(14+h)].
And then you divide that by h and get (14h-14h+h^2)/(196+14h), which is simplified to h^2/(196+14h).
My question is how do you get this into the format −1/(ah+b) if h^2 is in the numerator right now?
please explain and thanks
More Questions From This User See All
Answers & Comments
Verified answer
down to the third line you are ok - could simplify there since 14 - 14 + h = h
although you say "divide by h" you actually multiplied by it - that's where your error is
[f(5 + h) - f(5)]/h =
[1/(h + 14) - 1/14]/h
multiply 1/14 by (h + 14)/(h + 14) to get a common denominator
[1/(h + 14) - (1/14)(h + 14)/(h + 14)]/h =
[1/(h + 14) - ((1/14)h + 1)/(h + 14)]/h =
now put them over the same denominator
[(1 - (1/14)h - 1)/(h + 14)]/h
the 1 and -1 cancel
-[(1/14)h/(h + 14)]/h
now the first and last h cancel
-(1/14)/(h + 14) =
-1/(14(h + 14) =
-1/(14h + 14*14)