anonymous
  • anonymous
Can anyone find the tangent line approximation for f(x)=x^4+3x^2, when a =-1?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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myininaya
  • myininaya
f '(x)=4x^3+6x did you get this far?
anonymous
  • anonymous
ok i know how you got there
myininaya
  • myininaya
f '(1)=4+6=10

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More answers

myininaya
  • myininaya
10 is the slope of the tangent line at x=-1
myininaya
  • myininaya
so we know a point on the line and we know the slope of that line and a line has form y=mx+b f(-1)=10(-1)+b we can find b now 1+3=-10+b 4=-10+b 10+4=b 14=b so the tangent line is y=10x+14
anonymous
  • anonymous
For whatever reason the answers in the back of the book are telling me the tangent would equal -10x-6, is it possible we mixed signs along the way?
myininaya
  • myininaya
let me do it on paper one sec
myininaya
  • myininaya
is this what you are confused about? the answer in the back of the book? did you try this problem and get what I got?
myininaya
  • myininaya
oh i plug in 1
anonymous
  • anonymous
You didn't plug in -1
myininaya
  • myininaya
right polpak
anonymous
  • anonymous
No i got something like x^5+5x^4+7x^3+9x^2+6x because i thought it was F(x)=f(a)+f'(a)(x-a) inorder to solve this beast
myininaya
  • myininaya
f '(-1)=-10 not 10
myininaya
  • myininaya
y=-10x+b we need to know b we know a point on this line
anonymous
  • anonymous
Nah, just find the slope of the tangent and plug in that slope into point slope formula
anonymous
  • anonymous
Ok after you get the slope of the tangent what did you plug in to get you (x,y) values?
myininaya
  • myininaya
If x=1, then y=....
myininaya
  • myininaya
damn stupid 1
myininaya
  • myininaya
-1
anonymous
  • anonymous
\(x = -1 \implies f = x^4+3x^2 = ?\)
myininaya
  • myininaya
lol
anonymous
  • anonymous
thats 4 but we are stillnot jiving with the stupid books answer
myininaya
  • myininaya
we are fixing to
myininaya
  • myininaya
so we have y=-10x+b 4=-10(-1)+b
anonymous
  • anonymous
Take the slope (-10) and the point (-1,4) and plug into point slope. \(y-y_0 = m(x-x_0)\)
myininaya
  • myininaya
solve for b
myininaya
  • myininaya
you can use either way
anonymous
  • anonymous
Where m is the slope, \(x_0,y_0\) are the x and y for your point.
myininaya
  • myininaya
b=4-10=-6 so y=-10x-6
anonymous
  • anonymous
I like point slope cause I don't have to do anything else. Slope intercept is only useful if you're gonna graph it.
myininaya
  • myininaya
i like slope intercept its more fun to me for some reason
anonymous
  • anonymous
Ok where did we pull the y value from (4) sorry i missed how we came up with that one
anonymous
  • anonymous
Plug in x=-1 to the original equation for f(x)
anonymous
  • anonymous
Nevermind I'm sorry, I just figured that part out, thanks for the help guys. It has been a long day to put it nicely.

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