Question

find the equation of the tangent line to the graph of f(x)=cot(2x) at (π/4, 0)

Answer 1

Use Tangent line approximation for this

Answer 2

\[y = f(c) + f'(c)(x-c)\]

Answer 3

\[y = f(\frac{\pi}{4}) + f'(\frac{\pi}{4})(x-\frac{\pi}{4})\]

Answer 4

\[y = -2x + \frac{\pi}{2}\]

Answer 5

i think my teacher wants me to find the derivative of cot(2x) first

Answer 6

yes hero did that as well, just didn't write it

Answer 7

\[f'(x) = \frac{-2}{\sin^2(2x)}\]

Answer 8

I fogot

Answer 9

how did u find the derivative?

Answer 10

@shortie
is it clear what you need to do here? you want an equation for a line. to find an equation of a line you need two things
1) a point
2) the slope

you have the point, it is
\[(\frac{\pi}{4},0)\] so now you need the slope

Answer 11

ok

Answer 12

to find the slope you need to
a) take the derivative, which gives you a formula for the slope
b) plug in the x - value so that you actually get the number for the slope

Answer 13

then you use the point - slope formula or its equivalent, the formula that hero wrote up top

Answer 14

\[y = f(c) + f'(c)(x-c)\] is the point - slope formula rewritten. the point is
\[(c,f(c))\] and the slope is
\[f'(c)\] note that c and f(c) are numbers.

Answer 15

Good job hero

Answer 16

so when I plug (π/4) in, I'm going to get sin²(π/2) in the denominator?

Answer 17

i guess to but that is lucky because it is just 1, and so your slope is -1

Answer 18

no that is wrong, your slope is -2, sorry

Answer 19

hero wrote the answer above. you see that you have a line with slope -2. found by taking the derivative and plugging in the x - value

Answer 20

I got it! Thanks :)