Consider f:[1,∞)→R is given by f(x)=logex2-∫1ef(t)tdt, then which of the following is/are correct?

Sol. f(x)=ln2⁡x−16⇒f(e)=56f′(x)=2ln⁡xx≥0∀x∈[1,∞)f(x) is strictly increasing function f(1)=−16<0f′′(x)=21−ℓnxx2 Equation of tangent: y−56=2e(x−e)⇒y=2xe−76 Area =∫1e ln2⁡x−16−2xe−76dx=e+1e−3