Johan14th
  • Johan14th
{[3(x+h)^2 +(x+h)]- (3x^2+x)} / h
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Johan14th
  • Johan14th
\[\frac{ [3(x+h)^{2}+(x+h)]-(3x ^{2}+x) }{ h }\]
Vocaloid
  • Vocaloid
hint: use foil to expand (x+h)^2
Johan14th
  • Johan14th
Ive expanded it and tried to solve it but my answer is not a choice on my homework

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Vocaloid
  • Vocaloid
what did you get as the answer? you may have made a simple math error somewhere
Johan14th
  • Johan14th
i think the problem is my division after i distribute and cancel out like terms i get (6xh+3h^2+h)/h i get 6x +8h at the end
Vocaloid
  • Vocaloid
not quite, h should not be in the final answer at all. let's start from the beginning, ok?
Vocaloid
  • Vocaloid
|dw:1443578057830:dw|
Vocaloid
  • Vocaloid
|dw:1443578094689:dw|
Johan14th
  • Johan14th
okay so then it would be [3(x^2 + 2xh +h^2 ) + x+h -3x^2 -x]/h
Johan14th
  • Johan14th
alright so far so good
Vocaloid
  • Vocaloid
then we use distribution to expand the numerator|dw:1443578189706:dw|
Vocaloid
  • Vocaloid
then we cancel out terms|dw:1443578230609:dw|
Johan14th
  • Johan14th
i have a question does 3 not distribute to h^2 = 3h^2 ?
Vocaloid
  • Vocaloid
whoops
Vocaloid
  • Vocaloid
|dw:1443578317416:dw| (and I made a small mistake earlier, h should be in the answer. I was thinking of derivatives for some reason)
Vocaloid
  • Vocaloid
now, we factor out h from the numerator|dw:1443578421397:dw|
Vocaloid
  • Vocaloid
|dw:1443578448565:dw|
Johan14th
  • Johan14th
yeah this is actually trying to solve for a derivative using [f (x+h)- f(x)] / [(x+h)-x]
Vocaloid
  • Vocaloid
right, so if we're going for a derivative, all we need to do now is set h = 0
Johan14th
  • Johan14th
ohh so i have to factor out the 'h' okay and then the 0
Vocaloid
  • Vocaloid
|dw:1443578553000:dw|
Vocaloid
  • Vocaloid
so the derivative of 3x^2 + x = 6x + 1
Johan14th
  • Johan14th
Yessss this is an answer! thank you i have been trying to solve this for a while. thanks

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