Can anyone find the tangent line approximation for f(x)=x^4+3x^2, when
a =-1?

Question

Can anyone find the tangent line approximation for f(x)=x^4+3x^2, when 
a =-1?

myininaya · Answer

f '(x)=4x^3+6x did you get this far?

anonymous · Answer

ok i know how you got there

myininaya · Answer

f '(1)=4+6=10

myininaya · Answer

10 is the slope of the tangent line at x=-1

myininaya · Answer

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 · Answer

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 · Answer

let me do it on paper one sec

myininaya · Answer

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 · Answer

oh i plug in 1

anonymous · Answer

You didn't plug in -1

myininaya · Answer

right polpak

anonymous · Answer

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 · Answer

f '(-1)=-10 not 10

myininaya · Answer

y=-10x+b we need to know b
we know a point on this line

anonymous · Answer

Nah, just find the slope of the tangent and plug in that slope into point slope formula

anonymous · Answer

Ok after you get the slope of the tangent what did you plug in to get you (x,y) values?

myininaya · Answer

If x=1, then y=....

myininaya · Answer

damn stupid 1

myininaya · Answer

-1

anonymous · Answer

$x = -1 \implies f = x^4+3x^2 = ?$

myininaya · Answer

lol

anonymous · Answer

thats 4 but we are stillnot jiving with the stupid books answer

myininaya · Answer

we are fixing to

myininaya · Answer

so we have y=-10x+b
                4=-10(-1)+b

anonymous · Answer

Take the slope (-10) and the point (-1,4) and plug into point slope.

$y-y_0 = m(x-x_0)$

myininaya · Answer

solve for b

myininaya · Answer

you can use either way

anonymous · Answer

Where m is the slope, $x_0,y_0$ are the x and y for your point.

myininaya · Answer

b=4-10=-6
so y=-10x-6

anonymous · Answer

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 · Answer

i like slope intercept its more fun to me for some reason

anonymous · Answer

Ok where did we pull the y value from (4) sorry i missed how we came up with that one

anonymous · Answer

Plug in x=-1 to the original equation for f(x)

anonymous · Answer

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.