anonymous
  • anonymous
How do you find the linearization L(x) of f(x) = 3x^2+5x+12 at x=3? What are the steps for this?
Mathematics
chestercat
  • chestercat
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myininaya
  • myininaya
We need to find the tangent line of f at x=3
myininaya
  • myininaya
\[f'(x)=6x+15\] so to find the slope use f' and then we also know a point on the line \[(3,3(3)^2+5(3)+12=27+15+12=54)\]
myininaya
  • myininaya
\[y=mx+b => 54=23(3)+b \text{ solve for b}\]

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anonymous
  • anonymous
Wouldn't it be f'(x) = 6x + 17, when you take the derivitive?
myininaya
  • myininaya
oops i put an extra 1 in there lol
myininaya
  • myininaya
\[f'(x)=3(2x)+5=6x+5\]
myininaya
  • myininaya
\[(x^2)'=2x;(5x)'=5;(constant)'=0\]
anonymous
  • anonymous
Ok sounds good, also have another quick question, Where did you get the 23 from... on y=mx+b=>54=23(3)+b solve for b
myininaya
  • myininaya
well 23 was what i found when i plug into f' you know what i got earlier for f' lol
myininaya
  • myininaya
\[f'(3)=6(3)+5=18+5=23\]
myininaya
  • myininaya
f'(3) is the slope of the curve at x=3

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