Webwork 2.7-2.9 and assigment 5

WRITTEN ASSIGNMENT 5: DERIVATIVE APPLICATIONS

CALCULUS I, FALL 2022 MATH 1210-090

INSTRUCTOR: WILL FELDMAN

Name: uID:

Problem 1. Find the equation of the tangent line to the curve determined by the equation

yx2 + (x− y)3 = 2y + x− 3

at the point (1, 1).

Problem 2. (a) Find the linear approximation of x1/4 at x = 16.

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2 CALCULUS I, FALL 2022 MATH 1210-090 INSTRUCTOR: WILL FELDMAN

(b) Use part (a) to approximate 171/4.

Problem 3. A cowboy on his horse is herding a pair of cows in the desert when suddenly, at time t = 0 seconds, a desert gopher pops out of the ground and scares all the animals. The horse throws the cowboy off its back. One cow runs directly north at 8 meters per second the other cow runs directly east at 10 meters per second. When the cowboy gets back on his horse 10 seconds later how fast are the cows separating from each other?