In Exercises 40 through 49, assume that the required extreme value is a relative extremum.

Certain malignant tumors that do not respond to conventional methods of treatment such as surgery or chemotherapy may be treated by hyperthermia, which involves applying extreme heat to tumors using microwave transmissions.† One particular kind of microwave applicator used in this therapy produces an absorbed energy density that falls off exponentially. Specifically, the temperature at each point located r units from the central axis of a tumor and z units inside the tumor is given by a formula of the form

where A, p, q, and s are positive constants that depend on properties of both blood and the heating appliance (see the accompanying figure). At what depth does maximum temperature occur? Express your answer in terms of A, p, q, and s. You are not required to apply the second partials test.

Transcribed Image Text:

T(r, z) = Ae¯r (e-¯9² - e-s²)