Question

find an equation for the tangent line to the graph of f(x)=2cos(x)-sec(x) at the point (1/3pi,f(1/3pi))

Answer 1

So the equation of the tangent line is simply the derivative, do you know how to take the derivative of this function?

Answer 2

is it -(2+cos(2 x)) sec(x) tan(x)

Answer 3

i'm afraid not

Answer 4

what is the derivative of cos(x)

Answer 5

the derivative of f(x)=2cos(x)-sec(x) is -(2+cos(2 x)) sec(x) tan(x)

Answer 6

-sinx

Answer 7

did you actually compute the derivative or did you just get it off the internet?

Answer 8

the internet

Answer 9

wolframalpha is trusted

Answer 10

haha, that is the derivative.. But you don't know how they got that derivative.

Answer 11

lets do it together.

Answer 12

ok...

Answer 13

\[ f(x)=2\cos(x)-\sec(x)\]\[ f'(x)=(2\cos(x))'-(\sec(x))'\]

Answer 14

that 2 is just a constant so it will stay there.. all we need to compute is the derivative of cosx and secx

Answer 15

\[f'(x) = 2*(-\sin(x)) - (secx*tanx)\]

Answer 16

\[f'(x) = 2*\sin(x) + (secx*tanx)\]

Answer 17

ok..

Answer 18

Do you get that?

Answer 19

that still does not make an equation for 1/3pi,f1/3pi

Answer 20

we're not done yet

Answer 21

first we need to find out what f(pi/3) is

Answer 22

y

Answer 23

so we have our derivative, now to need to see what it is doing at the point (pi/3, f(pi/3))

Answer 24

f(x)=2cos(x)-sec(x)
f(pi/3) = 2 cos(pi/3) - sec(pi/3) = 2cos(pi/3) - 1/cos(pi/3)

Answer 25

ok

Answer 26

which = -1, so now we know our two points to evaluate our derivative at.. (pi/3, -1)

Answer 27

not to be rude and i really appreciate the explaination but i need to turn in the assignment i have tutoring tomorrow so i can get the explaination then

Answer 28

so do you think the answer is y-3sqrt3=1-sqrt3

Answer 29

the answer is -3sqrt(3)

Answer 30

you have to make an equation...

Answer 31

#10

Answer 32

which answer choice do u believe it is

Answer 33

hmm.. not sure.

Answer 34

wow ok