Question

How do I find the slope of the line tangent to a curve at a point?

Answer 1

use derivatives

Answer 2

@lgbasallote where'd you go?

Answer 3

i figured daniellerner was in good hands with you @saifoo.khan

Answer 4

So the derivative would be -sin(theta) then what

Answer 5

\[
\frac {y'(\pi/4)}{x'(\pi/4)}
\]

Answer 6

\[
x(\theta)= r(\theta) \cos(\theta)\\
y(\theta)= r(\theta) \sin(\theta)\\

\]

Answer 7

Why would you plug in pi/4?

Answer 8

\[
x(\theta )=\cos (\theta )
(\cos (\theta )+2)\\
y(\theta )=\sin (\theta )
(\cos (\theta )+2)
\]

Answer 9

To get the point (sqrt(2) +.5, sqrt(2) +.5)

Answer 10

I don't understand how pi/4 would get you there

Answer 11

Compute \( x(\pi/4) \)

Answer 12

Oh, I see

Answer 13

So the final answer would be -2?

Answer 14

No

\[
\sqrt{2}-2
\]

Answer 15

Are you sure you plugged them in correctly?

Answer 16

Yes

Answer 17

Yeah, you were right. I just messed up. Thanks

Answer 18

yw