Question

Find an equation for the tangent line to the graph of f(x) = arctanx at the point where x = 1

Answer 1

Find the slope of the curve at the point first.

Answer 2

Would it be \[1/\sqrt{2}\]

Answer 3

find \(f'(x)\)

Answer 4

evaluated at x = 1

Answer 5

That's what I attempted to do. lol. I tried it again, and using the formula from the textbook I got 0 this time. ><

Answer 6

\(\frac{d}{dx} [arctan(x)] = \frac{1}{x^2+1}\)

Answer 7

Oh! So m = 1?

Answer 8

1/2 I mean!

Answer 9

\[\frac{1}{x^2+1}|_{\left| _{x=1} \right|} = \frac{1}{2}\]

Answer 10

So y = (1/2) * 1 + b. What would y be?

Answer 11

why would u multiply 1+b? Where did that even come from?!

Answer 12

y = mx + b. I just plugged in m and x. O.O

Answer 13

well, \(\frac{1}{2}\) is your slope, so yes, m.

Answer 14

And x = 1, right? The only element I seem to need is y, then I could solve for b and give the equation for the tangent line at x = 1.

Answer 15

yes

Answer 16

Alright, so arctan(1) comes out to 45. So it would then be 45 = 1/2 +b --> 44.5 = b --> y = (1/2)x + 44.5. ... I think. xD

Answer 17

No. No. No.

y = \(\frac{1}{2}x+b\)

Answer 18

Why not give the b value?