B. A ladder 13 feet long rests against a vertical wall. If the top of the ladder slides down at a rate of 2ft/s, how fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 5ft above the ground?
B. A ladder 13 feet long rests against a vertical wall. If the top of the ladder slides down at a rate of 2ft/s, how fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 5ft above the ground?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 8CR
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Question 8B
Transcribed Image Text:8. The following two questions are applications of the derivative concept to real life situations.
Please recall our class discussions and do the following:
A. If z = 1(t) represents the position function at time t'of a certain particle, then what does
the derivative z(t) or represent?
B. A ladder 13 feet long rests against a vertical wall. If the top of the ladder slides down at a
rate of 2ft/s, how fast is the bottom of the ladder sliding away from the wall when the top of the
ladder is 5ft above the ground?
Note: Draw a large and clear sketch. You must erplain each step in order
receive credit.
9. The derivative of a given function f(z) is f'(z) = z² – 2.
a) What are the critical points of f(z)?
Note that it is the derivative of the given function that is stated above, and not the
actual function. This should be enough in order to compute the critical points.
b) Find the intervals of increase and decrease for the actual function f(z).
Note: You may want to draw a table and study the algebraic sign of f'(z), the way we did in
class.
c) Where do the local minimum and maximum values occur? Explain.
8
10. Let f(z) be an always negative function with the property that f'(z) <0 for any z.
a) Let g(z) = (f(z))". For what values of z will g(z) be increasing? Think about the
connection between increasing/decreasing functions and the algebraic sign of their
corresponding derivatives.
b) Let h(z) = f(f(z)). For what values of z will h(x) be decreasing?
11. Does the natural exponential function f(z) = e admit any inflection points? Explain why
or why not.
12. Now, recall our discussions with respect to indefinite and definite integrals, and do the
following:
a) State the most general antiderivative of f(E) =, i.e. compute the indefinite integral
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