Lukecrayonz
  • Lukecrayonz
@Psymon Okay a little different this time :O?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Lukecrayonz
  • Lukecrayonz
f(x+h)-f(x)/h Solve if f(x)=1-5x^3
Psymon
  • Psymon
Well, before we even start, one thing you should know. The "-f(x)" part ALWAYS cancels out. Whatever the "-f(x)" part is it better all go away or you did it wrong.
Lukecrayonz
  • Lukecrayonz
Okay :O I didn't know that but that makes sense now that I look at it.

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Lukecrayonz
  • Lukecrayonz
I haven't done this in a while, so to find f(x+h), you just simply put (x+h) where x is? So f(x+h)=1-5(x+h)^3?
Psymon
  • Psymon
So right, otherwise is the same thing as before, plugging in (x+h) in for x and then doing -f(x) \[\frac{ 1-5(x+h)^{3}-[1-5x ^{3}] }{ h } \]Now the cubed part is kind of annoying, but we can multiply it out the ong way or pascal's triangle with it. Either way, it should turn out like: \[\frac{ 1-5(x ^{3}+3x ^{2}h+3xh ^{2}+h ^{3})-(1-5x ^{3}) }{ h }\] \[\frac{ 1-5x ^{3}-15x ^{2}h-15xh ^{2}-5h ^{3}-1+5x ^{3} }{ h }\] And as planned, we get the 1 and the 5x^3 portions to cancel out: \[\frac{ -15x ^{2}h-15xh ^{2}-5h ^{3} }{ h }\]Factor out an h \[\frac{ h(-15x ^{2}-15xh-5h ^{2}) }{ h }\] \[-15x ^{2}-15xh - 5h ^{2} \]
Lukecrayonz
  • Lukecrayonz
Yikes! Thats still a bad equation to end with haha. One second let me write it down and see if I have questions
inkyvoyd
  • inkyvoyd
you can actually prove using factoring theorems that the end result cancels out certain parts if the expression if polynomial
Psymon
  • Psymon
Alrighty, lol.
Lukecrayonz
  • Lukecrayonz
Got it:)
Psymon
  • Psymon
Awesome :3
Lukecrayonz
  • Lukecrayonz
Okay so, next question the function is f(x)-3x^2-2x-1? How do I find f(x+h)
Psymon
  • Psymon
You would have to plug (x+h) into both x's in the function and then do the same thing.
inkyvoyd
  • inkyvoyd
subsitute all x's with (x+h)'s and evaluate the resulting expression
Lukecrayonz
  • Lukecrayonz
;_; Thats just so much work for nothing
inkyvoyd
  • inkyvoyd
unfortunately it is; in calculus you will learn a much faster way to do what you are doing - in more accurate words you learn the purpose of all of this.
Lukecrayonz
  • Lukecrayonz
I'm in applied calculus haha, this is just the first chapter. I haven't taken a math class in two years.
Lukecrayonz
  • Lukecrayonz
So f(x)=3x^2-2x-1 -3(x+h)^2-2(x+h)-1 -3(x+h)(x+h)-2x-2h-1 h^2+2hx+x^2=(x+h)^2 -3(h^2+2hx+x^2) [-3h^2-6hx-3x^2-2x-2h-1]-3x^2-2x-1 Cancel (-3h^2-6hx-2h)/h -3h-6x-2
Psymon
  • Psymon
I didnt work it out to see what the h-term should be, but the rest of it I guarantee is right. I doubt you made a mistake considering what ya got.

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