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anonymous
 4 years ago
How do you find the linearization L(x) of f(x) = 3x^2+5x+12 at x=3?
What are the steps for this?
anonymous
 4 years ago
How do you find the linearization L(x) of f(x) = 3x^2+5x+12 at x=3? What are the steps for this?

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myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1We need to find the tangent line of f at x=3

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[f'(x)=6x+15\] 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
 4 years ago
Best ResponseYou've already chosen the best response.1\[y=mx+b => 54=23(3)+b \text{ solve for b}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Wouldn't it be f'(x) = 6x + 17, when you take the derivitive?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1oops i put an extra 1 in there lol

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[f'(x)=3(2x)+5=6x+5\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[(x^2)'=2x;(5x)'=5;(constant)'=0\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ok 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
 4 years ago
Best ResponseYou've already chosen the best response.1well 23 was what i found when i plug into f' you know what i got earlier for f' lol

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[f'(3)=6(3)+5=18+5=23\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1f'(3) is the slope of the curve at x=3
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