Pharmacy exam 2016-11-07
Degrees: Pharmacy and Biotechnology
Date: Nov 7, 2016
Question 1
The amount
- Compute the equations of the tangent and normal lines to the graph of
as a function of at the point . - Compute the approximate change of the amount
if changes by 2mg, from the same point .
- Tangent line:
.
Normal line: . mg.
Question 2
The temperature at a point
Suppose we are position at
- In which direction will the temperature decrease the fastest? What will be the rate of that decrease? What is the meaning of your result?
- Compute the directional derivative in the direction where
increases twice as much as , and increases half of . What is the meaning of your result?
. The rate of decrease is .- Taking the vector
, . This means that for each unit in the direction of the vector the function will increase units.
Question 3
Allometric growth refers to relationships between sizes of different parts of an organism. Suppose
- Compute the differential equation that explains
as a function of (that is, take as the independent variable and as the dependent one). Solve the equation for . - Assume
denotes the mass of a cell, and its volume, with , compute as a function of if m at the age at which is equal to 1 ng.
- Differential equation:
.
General solution: . - Particular solution:
.
Question 4
Find the local extrema and saddle points of the function