In a case of Plasmodium falciparum malaria, the peripheral blood smear does not demonstrate trophozoites and schizonts. The reason for this is:

-Plasmodium falciparum is associated with infected red cells expressing PfEMP (Plasmodium falciparum erythrocyte membrane protein) leading to their attachment to the endothelial cells. -This leads to sequestration of infected red cells in the capillaries. -That's the reason for the non-appearance of trophozoites and schizonts in the peripheral blood smear.