if you look super closely at the black spots, are they from bugs or from soil on the leaf? The burnt tip can be from a few things. If the tip gets too cold or damaged it can die off like that. Generally nutrient burn will show on the whole leaf so I dont think it is that. Is it only on this leaf? how does the rest of the plant look. if the rest of the plant is looking fine and healthy then it is probably nothing to worry about.