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

2024
Views:

360

Pages:

1
Author:

vykolsinaigr

Workshop #19 1. The graph of y = f (x) is shown below. (a) For what values of x is f 0 (x) = 0? (b) For what values of x is f 0 (x) undefined? (c) Find all intervals where f 0 (x) > 0. (d) Find all intervals where f 0 (x) < 0. 2. Suppose g(x) is some function and you know that g 0 (x) > 0 on (−∞, 3) and g 0 (x) < 0 on (3, ∞). What must be true about g 0 (3)? 3. Let f (x) = x2 + 4 . x (a) Determine the intervals on which f is increasing or decreasing. (b) Use this information to locate any local maxima or minima for f . 4. Let g(x) = (x2 − 9)2 . (a) Determine the intervals on which g is increasing or decreasing. (b) Use this information to locate any local maxima or minima for g. 5. Let h(x) = x(x2 − 9). (a) Determine the intervals on which h(x) > 0 and on which h(x) < 0. (b) Determine the intervals on which h0 (x) > 0 and on which h0 (x) < 0. (c) Find all local maxima and minima for h. (d) Use the results from above to sketch a graph of h. 6. Let k(x) = x3 . x2 − 3 (a) Determine the intervals on which k is increasing or decreasing. (b) Use this information to locate any local maxima or minima for k.