Question

need help finding the equation of a tangent line?

Answer 1

f(x) = 4sec(x) - 8cos(x)

f ' (x) = ???

Answer 2

4sec(x)tan(x)-8(-sinx) ??? not sure

Answer 3

correct, which simplifies to 4sec(x)tan(x)+8sin(x)

Answer 4

then you use that to compute f ' (pi/3) to get the slope of the tangent line at x = pi/3

Answer 5

which gives you the value of m (the slope)

Answer 6

oh you plug it in?

Answer 7

yes pi/3 into f ' (x)

Answer 8

is the answer

Answer 9

that is the value of m

Answer 10

now you need to find b

Answer 11

(x,y) = (pi/3, 4)

x = pi/3
y = 4
m = 12*sqrt(3)


y = mx+b

4 = 12*sqrt(3)*pi/3 + b

solve for b

Answer 12

if i did my math right is it -17.77?

Answer 13

approximately, yes

Answer 14

you can also write b in exact form


\[\Large 4 = 12\sqrt{3}*\frac{\pi}{3} + b\]


\[\Large 4 = \frac{12\pi\sqrt{3}}{3} + b\]


\[\Large 4 = 4\pi\sqrt{3} + b\]


\[\Large 4 - 4\pi\sqrt{3} = b\]


\[\Large b = 4 - 4\pi\sqrt{3}\]

Answer 15

thank you very much :)

Answer 16

you're welcome