X intercept (6,0)
y intercept (-3,0)
slope is m= 1/2
F(x) = x - 2sinx
To find for what values of x graph has tangents we need to differentiate function f(x).
f'(x) = 1-2cosx
Now, if we want to have horizontal tangents we need to make function f'(x) equal to 0 because at minimum or maximum of function f(x) tangent is horizontal.
1-2cosx = 0
cosx = 1/2
x = pi/3 + 2*n*pi and
x = -pi/3 + 2*n*pi
Explanation: cosx = 1/2 for both 60° and -60°. If we make one circle cosx will be equal to 1/2 for 420 and 300 degrees. Writing degrees in radians (using pi) we can write formulas above where 2*pi represents one full circle and n is an integer which represents how many circles we made.
The answer is 11.2 pounds.
