## anonymous 5 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?

1. myininaya

We need to find the tangent line of f at x=3

2. myininaya

$f'(x)=6x+15$ so to find the slope use f' and then we also know a point on the line $(3,3(3)^2+5(3)+12=27+15+12=54)$

3. myininaya

$y=mx+b => 54=23(3)+b \text{ solve for b}$

4. anonymous

Wouldn't it be f'(x) = 6x + 17, when you take the derivitive?

5. myininaya

oops i put an extra 1 in there lol

6. myininaya

$f'(x)=3(2x)+5=6x+5$

7. myininaya

$(x^2)'=2x;(5x)'=5;(constant)'=0$

8. 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

9. myininaya

well 23 was what i found when i plug into f' you know what i got earlier for f' lol

10. myininaya

$f'(3)=6(3)+5=18+5=23$

11. myininaya

f'(3) is the slope of the curve at x=3