Critical Numbers and Absolute Extremes

Explore critical numbers and absolute extremes in this comprehensive 90-minute video tutorial. Learn to find critical numbers for various functions, including rational, exponential, and trigonometric expressions. Discover techniques for determining absolute minimums and maximums on closed intervals. Work through multiple examples, such as finding the critical numbers of (y-1)/(y^2-y+1), x^2*e^(-3x), and 2cos(x)+sin^2(x). Practice solving problems involving absolute extrema for functions like ln(x^2+x+1) on [-1, 1] and x+1/x on [0.2, 4]. Gain a deeper understanding of local and absolute extrema through solved exercises from textbook section 4.1.

Critical number of (y-1)/(y^2-y+1).
Critical number of a t^(3/4)-2t^(1/4).
Critical number of a x^(4/5)*(x-4)^2.
Critical number of a x^2*e^(-3x).
Find the critical numbers of 2cos(x)+sin^2(x).
abs min and ABS MAX of ln(x^2+x+1) on [-1, 1].
abs min and ABS MAX for x+1/x on [0.2, 4].
abs min and ABS MAX of 2cos(t)+sin(2t), (2014 version).
abs min and ABS MAX for 2cos(t)+sin(2t), full details! (2018 version).
ABS MAX of sin(x)-sin^2(x).
Absolute min/max, local min/max, sect 4.1 #7.
Absolute min/max, local min/max, sect 4.1 #9.
Absolute min/max, local min/max, sect 4.1 #11.
Absolute min/max, local min/max, sect 4.1 #13.