Question

Find an equation of the tangent line to the graph of the function f(x) = 2sinx at the point where x = pi/3.

Answer 1

ok in order to find tangent line we have to take the derivative and so we will find the slope of the tangent line

what is the derivative of f(x) = 2sin(x) ?

Answer 2

2cosx

Answer 3

that's good.. f'(x) = 2cos(x)
now since we want the tangent to the function at the point x=pi/3
in order to find the slope of the tangent we have to plug x=pi/3 into the derivative

f'(pi/3) = ?

Answer 4

1?

Answer 5

yes so we have a slope for the tangent line m= 1.

Answer 6

the last thing that we will need is a point on the tangent line so we could find its equation
since the tangent line touches the graph at x=pi/3 we can get a y value from the original function f(x). so we will have a point (pi/3,f(pi/3))

Answer 7

so f(pi/3) = 2sin(pi/3) = sqrt(3)

now we have a point (pi/3,sqrt(3)) and a slope m =1

using the formula for line equation
y=y1 + m(x-x1)
can you find the tangent line ?

Answer 8

ill give the answer since i have to go but try it by yourself as well :
y = sqrt(3) + x - pi/3
y= x +sqrt(3)-pi/3

Answer 9

thanks! i got it :)