MATH116 Lecture Notes - Lecture 4: Opata Language, Asymptote, Inflection Point

• School: University of Waterloo
• Department: Mathematics
• Course: MATH116
• Professor: Fiona Dunbar

Document Summary

, so we look at the intervals of the real. 3+x) < 0, and x4 > 0, so the product/quotient x4 = ( Solution: (a) f(cid:48)(x) = x3(2x) (x2 1)(3x2) line split up at x = . 3 x) > 0, ( that makes up f(cid:48)(x) is negative, which means f is decreasing on ( , . 3 x) > 0, ( that makes up f(cid:48)(x) is positive, which means f is increasing on ( . 3), we have ( that makes up f(cid:48)(x) is positive, which means f is increasing on (0, 3, ), we have ( that makes up f(cid:48)(x) is negative, which means f is decreasing on ( (b) there is a local minimum at x = : the y-value is f ( , = 3 1. 3 x) > 0, : the y-value is f ( 3 + x) > 0, and x4 > 0, so the product/quotient. There is a local maximum at x =