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

2024
Views:

47

Pages:

1
Author:

Avery Benjamin

Workshop #11 1. Consider the function f (x) = (1 + ex )(x − 1). We will compute the derivative of this function in two different ways. (a) Use the product rule to compute f 0 (x). (b) Multiply the binomials in f (x) first, then compute f 0 (x). (c) Which method did you prefer? 2. Find the derivative of each of the following functions. (a) f (x) = (x2 − 3x)ex √ (b) f (x) = 3 x · ex 2x √ (c) f (x) = 2+ x 3. At what points on the graph of f (x) = x3 + x2 is the tangent line parallel to the line y = 16x − 7? 4. Where does the normal line to the parabola y = x − x2 at the point (1, 0) intersect the parabola a second time? 5. Find the equations of all the lines through the point (3, 1) that are tangent to the graph of y = x . x+1