anonymous
  • anonymous
Compute and simplify the difference quotient f(a+h)-f(a) --------- h g(x)=2x^2+14x -13
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
this was already confusing enough without changing it to g(x)
anonymous
  • anonymous
replace \(g\) by \(f\) it makes no difference, it is all algabra
anonymous
  • anonymous
oh ok. so it's like: 2(a+h)^2+14(a)-13 over h?

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anonymous
  • anonymous
which comes to...
anonymous
  • anonymous
no hold on
anonymous
  • anonymous
oh
anonymous
  • anonymous
you have to subtract first
anonymous
  • anonymous
well, first you have to expand, then you have to subtract
anonymous
  • anonymous
\(g(a+h)= 2(a+h)^2+14(a+h)-13\)
anonymous
  • anonymous
expand like 2a+2h.... and so on?
anonymous
  • anonymous
(2a+2h)^2?
anonymous
  • anonymous
for the first one
anonymous
  • anonymous
yeah it is \[2(a^2+2ah+h^2)+14a+14h-13\] \[=2a^2+4ah+2h^2+14a+14h-13\]
anonymous
  • anonymous
square first multiply by 2 second
anonymous
  • anonymous
oh ok, gotcha
anonymous
  • anonymous
from this you need to subtract \(2a^2+14a-13\) so everything without an \(h\) will be gone
anonymous
  • anonymous
then you can factor out an \(h\) from the remaining terms in the numerator, and cancel with the \(h\) in the denominator
anonymous
  • anonymous
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
anonymous
  • anonymous
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?
anonymous
  • anonymous
subtract
anonymous
  • anonymous
\(2a^2-2a^2=0\) \(14a-14a=0\) and \(-13-(-13)=0\)
anonymous
  • anonymous
in other words, every term without an \(h\) is gone
anonymous
  • anonymous
oh, now I get it
anonymous
  • anonymous
and that leaves me with 4ah + 2h^2 +14h
anonymous
  • anonymous
yes, and now divide by \(h\)
anonymous
  • anonymous
as you said lol
anonymous
  • anonymous
ok
anonymous
  • anonymous
4a+2h+14
anonymous
  • anonymous
which is one of my multiple choice answers...
anonymous
  • anonymous
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

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