Question

I am asked to find the equation of the tangent line to the curve f(x)=sin(x)+sin^2(x) at the point (0,0). Can anyone explain how I should approach this problem? I understand that I must differentiate the function, but I can't see how to come up with the equation for the line. Any help would be greatly appreciated.

Answer 1

can you find the derivative?

Answer 2

equation of the line:
y = mx+b

m = f'(0) **slope is derivative at point (0,0)
b = y-mx = 0-f'(0)*0 = 0

--> y = f'(0)x

all you need to do is find f'(x)

Answer 3

slope point form:
slope=m
point: (x,y)
y-y2=m(x-x1)

slope=f'[0]
point: (0,0)
y-0=(f'[x])(x-0)