All aperture settings on your lens are not created equal! Some are sharper than others. In fact, it can be very easy to buy a used lens and conclude that it is not sharp simply because you are using the wrong aperture setting. No lens is equally sharp at all aperture settings. The laws of physics make that impossible. The difference between the sharpest and the softest aperture can at times be quite distinct.
Here’s a couple of test shots (unsharpened) I made using a vintage (1978) Tokina RMC 35-135mm F:4 – F:4.5 lens I recently purchased on eBay for $5.00. The lens and camera were tripod mounted and I was approximately 12 feet from the subject with the lens set at 135mm. The first shot was taken at F:4, this lens fastest aperture. The second was taken at F:11. Other than the camera setting the shutter speed automatically, no other adjustments were made. At F:4 the lens produces a very soft image while at F:11 sharpness and contrast has improved dramatically. If I want the sharpest images from this lens, I need to shoot at F:11.
Generally, most lenses are designed to be their sharpest at around F:8 to F:11. Typically, kit lenses and short telephoto lenses are usually designed to deliver the sharpest images at these apertures. Faster lenses are sometimes designed to deliver sharper results at around F:5.6. The best way to know is to test it yourself. Tape a page of print from a newspaper to a flat wall and shoot images from a fixed position on a tripod mounted camera at each aperture setting. Look at each image at 100% size on your computer display. It will be easy to discern which settings are the sharpest. -Don Peterson