University:
University of North Dakota
Course:
Math 165 | Calculus I
Academic year:

2024
Views:

457

Pages:

1
Author:

Baylee Callahan

Workshop #20 1. Sketch a graph that satisfies all of the following criteria. • f (x) is continuous • f (−4) = 0 and f (x) does not equal zero anywhere else • f 0 (x) > 0 on the intervals (−∞, −1) and (2, ∞) • f 0 (x) < 0 on the interval (−1, 2) • f 0 (−1) is undefined and f 0 (2) is undefined 2. Sketch a graph that satisfies all of the following criteria. • f (x) is continuous • f (−2) = 0, f (1) = 0 and f (x) does not equal zero anywhere else • lim f (x) = 3 x→∞ • lim f (x) = ∞ x→−∞ • f 0 (x) < 0 on the intervals (−∞, −1) and (0, 12 ) • f 0 (x) > 0 on the intervals (−1, 0) and ( 12 , ∞) 3. Find the absolute maximum and minimum of the following functions on the given interval. (a) f (x) = sin x, 0 ≤ x ≤ π 2 (b) f (x) = 2x3 − 3x2 − 12x + 1, [−2, 3] (c) f (x) = x − ln x, [ 12 , 2] 4. Show that the function f (x) = x101 + x51 + x + 1 has neither a local maximum or a local minimum. 5. For each of the problems below, sketch a graph of a function that is continuous on [1, 5] and has the given properties. (a) Absolute minimum at 2, absolute maximum at 3, local minimum at 4 (b) No local maximum or minimum, but 2 and 4 are critical numbers (c) Absolute maximum at 5, absolute minimum at 2, local maximum at 3, local minima at 2 and 4