An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the?

opening is modeled by the function f(x)=8sinx+2. in the interval 0 is less than or equal to x which is less than or equal to pie (90 deg.) where x is expressed in radians. sove algebraically for all values of x in the previous interval where the height of the opening f(x) is 6. If the x-axis represents the base of the tunnel what is the maximum height of the entrance of the tunnel?

Public Comments

1. 6=f(x)=8sinx+2 1/2 = sinx where x is between 0 and pi (which is 180 deg btw) x=pi/6 or x=5pi/6 f'(x)=8cosx = 0 x bet 0 and pi x=pi/2 f(pi/2) = 8sin(pi/2)+2 = 10 f(0)=0 f(pi)=0 Therefore the maximum height of 10 is achieved at x=pi/2.