Practical Applications in Calculus

Question

(Applicable to an Internal Medicine or its equivalent case).

As blood moves from the heart through the major arteries out the capillaries and back through the veins, as expounded by a Professor to his/her class, the systolic pressure continuously drops. Suppose that this pressure is given by the model below,

P = 25t^2 + 125 / t^2 + 1 , 0 ≤ t ≤ 10

where P is measured in millimeters of mercury and t is measured in seconds. At what rate is the pressure changing 5 seconds after blood leaves the heart?

Answer 1

Determine P'(t).

Set P'(t) = 0 and solve for t.