Problem 1 With constant parameters 7 > 0 and wo, define a function S by (1/T)2 S ( w ) = - ( w - wo) ? + (1 / 7 ) 2 (1) (1.1) Find a value of w where S (w) = 1/2. (1.2) Calculate the derivative, S', of the function S: find a formula for S" (w). (1.3) Identify all the stationary points of S: solve the equation S' (w) = 0. (1.4) Calculate the value, S (w), at each stationary point of S. (1.5) Calculate the second derivative, S", of S: find a formula for S" (w). (1.6) Identify all the flexes of S: solve the equation S" (w) = 0. (1.7) Calculate the value, S (w), at each flex of S. (1.8) Determine whether the flexes of S are points of inflection. (1.9) Identify the horizontal asymptotes of S: find lim S (w) and lim S (w). (1.10) Make a plot of S that includes the stationary points and the flexes