Chemotaxis is the directed motion of organisms in response to the chemical gradient. When E. coli bacterium is placed in a medium with a concentration gradient of nutrient, it moves up the gradient and accumulates in regions with higher nutrient concentration. The efficient chemotactic performance is characterised by the ability to find the favorable region quickly and to localize in the favorable region at large times. We investigate how this efficiency depends on the external environment and the internal biochemical pathway of the E.coli cell. When the cell is in a medium where the nutrient is diffusing and the form of nutrient profile is Gaussian, we find that there exists an optimal width of the profile for which the search time becomes minimum. In the case when the nutrient diffusion and cell movement occurs over comparable time-scales, there exists an optimum value of the nutrient diffusivity for which the search time becomes minimum. The simulation results in a phenotype

	model agree well with our analytical calculations in a related coarse-grained model where the bacterium behaves like a random walker with position dependent drift velocity and diffusion coefficient. In a single cell chemotaxis the internal biochemical pathway involves noise due to the fluctuations present in the number of different molecules taking part in the reactions. This noise plays a very crucial role on the chemotactic performance of E. coli bacterium. We find that in the long time limit the  localization and the uptake, i.e. the total nutrient intercepted along its trajectories, becomes maximum for an optimum value of the noise strength. We discuss a simple mechanism to explain this effect.