CAS MA 123 Lecture Notes - Lecture 20: Maxima And Minima, 32X

• School: Boston University
• Department: Mathematics & Statistics
• Course: CAS MA 123
• Professor: John Bergdall

Document Summary

Ma123 lecture 20 finding absolute extreme values. A critical point x=c is a point in the interior of the domain of f(x) where f"(c) =0 or f"(c) = dne. To find absolute extreme values examine the values. What the table is missing is whether or not x=1 is a local extreme value or not. Definition: f(x) defined on an interval i: say f(x) is increasing on i if x1 < x2 are points in i >>> f(x1)f(x2) F(x) = x2 is increasing on [0, ) Converse statements are not true f(x)= x3 is increasing (- , ) but f"(x)>0 only on (- ,0) and (0, ) F(x) = 2x3 -15x2 + 24x f"(x)=6x2 30x +24. Analyze sign of f"(x)= 6(x-1)(x-4) f"(x) = 0 at x= 1,4. Since derivative is continuous here the sign doesn"t change on (- ,1) (1,4) (4, )