Show by example that these statements are false: (a) If a function…
Show by example that these statements are false:
(a) If a function reaches its maximum and minimum then the function is continuous.
(b) If reaches its maximum and minimum and all values between and , it is continuous at .
(c) (mostly for instructors) If has the intermediate value property between all points and , it must be continuous.
Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.7 Continuous Functions, #37
No hints for this one.
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