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

- anonymous

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

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- myininaya

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

- anonymous

ok i know how you got there

- myininaya

f '(1)=4+6=10

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- myininaya

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

- 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

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

let me do it on paper one sec

- 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

oh i plug in 1

- anonymous

You didn't plug in -1

- myininaya

right polpak

- 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

f '(-1)=-10 not 10

- myininaya

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

- anonymous

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

- anonymous

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

- myininaya

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

- myininaya

damn stupid 1

- myininaya

-1

- anonymous

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

- myininaya

lol

- anonymous

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

- myininaya

we are fixing to

- myininaya

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

- anonymous

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

- myininaya

solve for b

- myininaya

you can use either way

- anonymous

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

- myininaya

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

- 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

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

- anonymous

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

- anonymous

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

- 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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.