StudyGurl14
  • StudyGurl14
PLEASE HELP! MEDAL! @solomonzelman
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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StudyGurl14
  • StudyGurl14
1 Attachment
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle f(x)=\sqrt{x^2+9} }\) \(\large\color{#000000 }{ \displaystyle a=-4 }\)
SolomonZelman
  • SolomonZelman
basicaly, you are finding the tangent line to the function, at the point x=a, AND THEN you are using this tangent line to approximate f(a).

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StudyGurl14
  • StudyGurl14
ok, so first find the derivative...|dw:1449705797522:dw|
StudyGurl14
  • StudyGurl14
right?
StudyGurl14
  • StudyGurl14
then plug in -4 for x?
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle f(x)=\sqrt{x^2+9{\color{white}{\Large |}} } }\) \(\large\color{#000000 }{ \displaystyle f'(x)=? }\)
StudyGurl14
  • StudyGurl14
|dw:1449705904502:dw|
SolomonZelman
  • SolomonZelman
yes, very good
StudyGurl14
  • StudyGurl14
now plug in -4?
SolomonZelman
  • SolomonZelman
yes you plug in -4 into f'(x) to find the instantaneous slope of the function at x=-4.
StudyGurl14
  • StudyGurl14
so, you'd get \(\Large-\frac{4}{5}\)
StudyGurl14
  • StudyGurl14
for the slope, right?
SolomonZelman
  • SolomonZelman
yes
StudyGurl14
  • StudyGurl14
now what?
SolomonZelman
  • SolomonZelman
then, you have to find f(-4)
StudyGurl14
  • StudyGurl14
5
SolomonZelman
  • SolomonZelman
Wait I need to go over everything ... I am never in my right mind after basketball
StudyGurl14
  • StudyGurl14
f(-4) = 5 So, for the line...you get y = (-4/5)x + b (5) = (-4/5)(-4) + b 5 = -16/5 + b 42/5 = b Is that right?
StudyGurl14
  • StudyGurl14
I have to go. I'll be back tomorrow.
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle L(x)=f'(a)\cdot (x-a)+f(a)}\)
StudyGurl14
  • StudyGurl14
Oh, ok, thanks
StudyGurl14
  • StudyGurl14
so (-4/5)(x - a) + 5 wouldn't (x - a) = 0?
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle y=(-4/5)(x+4)+5}\) this is what I get. https://www.desmos.com/calculator/fmdldsjksx
StudyGurl14
  • StudyGurl14
ah, you leave the x term. thanks
SolomonZelman
  • SolomonZelman
and then you plug in -4+0.1
SolomonZelman
  • SolomonZelman
didn't you need to find f(-4+0.1) ?
SolomonZelman
  • SolomonZelman
For linearization (a), you leave the x. (you need the tangent line at x=a) For (b), you need to find f(a+0.1), which will be f(-3.9).
SolomonZelman
  • SolomonZelman
YOu need to plug in -3.9 into the tangent line

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