Plz solve q6 Plz solve q6 S. 6. Range of tbc function Ax) (cost 1 (a) {c) (0.1n2) (b) (d) of 12. 13. 14. Tie 2 is given Which or Range of by f (x) ' bere and denote the greatest Share with your friends Share 0 Vijay Kumar Gupta answered this Dear Student, Consider the following function. fx=ln cosxcosx+1Note that the range of the function depends entirely on the values of cosxcosx.The function takes its minimum and maximum value according to as takes itsminimum and maximum value. We know that range of cosine function is -1,1.This gives, -1≤cosx≤1This implies that, cosxcosx≤1cosx⇒cosxcosx≤1⇒cosxcosx+1≤1+1=2⇒lncosxcosx+1≤ln2 ....1Thus, the maximum value of the function is ln2.To find the minimum value of the function, we will find the minimum value of the function y=cosxcosx.Take log on both sides of y=cosxcosx to get, lny=cosx lncosxDifferentiate both sides with respect to x. 1y dydx= lncosx·ddxcosx+cosx·ddxlncosx = lncosx·-sinx+cosx·1cosx-sinx =-sinxlncosx+1⇒dydx=- cosxcosxsinxlncosx+1The critical point is given by, dydx=0⇒lncosx+1=0 Since cosxcosxsinx ≠0 ⇒lncosx=-1 ⇒cosx=e-1This can be shown using first or second derivative test that y=cosxcosx takes its minimum value when cosx=e-1.Thus, the minimum value of fx is, fx=ln cosxcosx+1≥ln e-1e-1+1⇒fx≥ln 1+1e1e ....2From 1 and 2, the range of given function is ln 1+1e1e, ln2 Regards 1 View Full Answer Vinay answered this sorry i cant see it properly. 0
