MAT 1300 Lecture Notes - Lecture 8: Maxima And Minima, Implicit Function

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Dongyang Kuang

Document Summary

*note: go over the exam review that is now posted on brightspace. Learning goals for this lesson: chain rule, implicit differentiation, maximum and minimums, short example of an absolute function. Recall from the last lesson that the chain rule deals with the composition of f and g, (f g)1. A saying to remember this is: derivative of the outside, with the inside staying the same, times the derivative of the inside". We can simplify the final answer by multiplying the coefficient in front of the first bracket by the second bracket (in this case, multiplying 20 by 12x2) It is called implicit because the function is not given to us. An explicit form of a function is one in which one variable is expressed in terms of the other. Explicit: y= f(x)*note: dy/dx can be interchangeable with y1. Step 1: differentiate both sides of the equations with respect to x. Step 2: solve for dy/dx by isolating it.