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Compute and simplify the difference quotient
f(a+h)f(a)

h
g(x)=2x^2+14x 13
 one year ago
 one year ago
Compute and simplify the difference quotient f(a+h)f(a)  h g(x)=2x^2+14x 13
 one year ago
 one year ago

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brandonlovesBest ResponseYou've already chosen the best response.0
this was already confusing enough without changing it to g(x)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
replace \(g\) by \(f\) it makes no difference, it is all algabra
 one year ago

brandonlovesBest ResponseYou've already chosen the best response.0
oh ok. so it's like: 2(a+h)^2+14(a)13 over h?
 one year ago

brandonlovesBest ResponseYou've already chosen the best response.0
which comes to...
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you have to subtract first
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
well, first you have to expand, then you have to subtract
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\(g(a+h)= 2(a+h)^2+14(a+h)13\)
 one year ago

brandonlovesBest ResponseYou've already chosen the best response.0
expand like 2a+2h.... and so on?
 one year ago

brandonlovesBest ResponseYou've already chosen the best response.0
for the first one
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
yeah it is \[2(a^2+2ah+h^2)+14a+14h13\] \[=2a^2+4ah+2h^2+14a+14h13\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
square first multiply by 2 second
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
from this you need to subtract \(2a^2+14a13\) so everything without an \(h\) will be gone
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
then you can factor out an \(h\) from the remaining terms in the numerator, and cancel with the \(h\) in the denominator
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you should be left with \[4ah +14h+2h^2\] before you divide after you divide you get \[4a+14\] and next week you will be able to do this problem instantly in your head
 one year ago

brandonlovesBest ResponseYou've already chosen the best response.0
ok, so I have 2a^2 +4ah + 2h^2 +14a +14h 13 and then I subtract 2a2+14a−13? how do I know to do that?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\(2a^22a^2=0\) \(14a14a=0\) and \(13(13)=0\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
in other words, every term without an \(h\) is gone
 one year ago

brandonlovesBest ResponseYou've already chosen the best response.0
and that leaves me with 4ah + 2h^2 +14h
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
yes, and now divide by \(h\)
 one year ago

brandonlovesBest ResponseYou've already chosen the best response.0
which is one of my multiple choice answers...
 one year ago

brandonlovesBest ResponseYou've already chosen the best response.0
well, I dunno if I'll be able to do that in my head instantly, but if I can work it out, then I'll be ok at least haha. Thanks @satellite73
 one year ago
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