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

2024
Views:

224

Pages:

1
Author:

inao6uk

Workshop #18 1. Differentiate the following functions: (a) f (x) = x2 sin(x2 ) (b) g(x) = ln(x + ecos x ) √ 3 x (c) h(x) = ln x (d) j(x) = tan2 (x2 ) + ln(ex + 1) √ (e) l(x) = e ln(5−x) √ 2. Find an equation for the tangent line to graph of the curve given by x2 y + x y = (x + y)2 − 3 at the point (2, 1). 3. Find all points on the graph of y = x2 e−3x where the tangent line is horizontal. √ 4. Use a tangent line approximation to estimate 5 33. 5. Sketch a graph that satisfies all of the following criteria. • 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) = 0 and f 0 (2) = 0 6. Sketch a graph that satisfies all of the following criteria. • f (−4) = 0 • lim f (x) = −∞ • x→2 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