Calculus of a Single Variable, Chapter 2, 2.4, Section 2.4, Problem 72

Hello!
y(x) = (1/x) + sqrt(cos(x)) .
cos(x) must be >=0 and cos(x) < 0 for pigtxgtpi/2 (at the right neighborhood of pi/2 ). So there can be only the left derivative.
Check that y(pi/2) = 2/pi :cos(pi/2) = 0 and y(pi/2) = 2/pi + 0 = 2/pi .
Next, find the derivative of y:y'(x) = -(1/x^2) + (1/2)*(cos(x))^(-1/2)*(-sin(x)) .
For x-gtpi/2-0
y'(x) ->-oo
(1/x^2 is finite, sin(x) is finite and (cos(x))^(-1/2)-gt+oo )
and therefore the tangent line is vertical, its equation is x=pi/2 .
The graph is here: https://www.desmos.com/calculator/4owqqw7egh