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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 x
1/4 at x = 16.
1
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?
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