MRN11 CC HW#13: Speeds, Rates, and DerivativesName:Part A. Meaningful MathThe derivative of a functionat a point is one of thebasic concepts of calculus.If a function is definedby the equationy = f(x) and (a, b) is apoint on the graph, thenthe derivative of f at(a, b) can be thought of inat least two ways.• It is the slope of the linethat is tangent to thecurve at (a, b).• It is the instantaneous rate at which the y-value of the function ischanging as the x-value increases through x = a. We often call thisthe derivative at x = a rather than the derivative at (a, b).In this activity, you will work with this new idea in connection withsome familiar situations. Keep in mind that you can find derivatives byusing smaller and smaller intervals around a particular value of a.1. The function h(t) = 400 – 16ť gives the height of the supply bundle(in feet) t seconds after it is dropped from a height of 400 feet.a. Find the derivative of this function at the point (3, 256).b. What does your answer tell you about the speed at which thesupply bundle is falling?2. The function A(t) = ¤(70 + 6t)² gives the area of the oil slick (insquare meters) t hours after Lindsay first spots it.a. Find the rate at which the area is growing exactly one hour afterLindsay first saw it.b. Express your answer as a derivative.

Answered: Image /qna-images/answer/54168b30-a637-4c99-af53-a5cc132d49d4.jpg

1. The function h(t) = 400 – 162 gives the height of the supply bundle (in feet) t seconds after it is dropped from a height of 400 feet. a. Find the derivative of this function at the point (3, 256). b. What does your answer tell you about the speed at which the supply bundle is falling?

1. The function h(t) = 400 – 162 gives the height of the supply bundle (in feet) t seconds after it is dropped from a height of 400 feet. a. Find the derivative of this function at the point (3, 256). b. What does your answer tell you about the speed at which the supply bundle is falling?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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Question

MRN11 CC HW#13: Speeds, Rates, and Derivatives
Name:
Part A. Meaningful Math
The derivative of a function
at a point is one of the
basic concepts of calculus.
If a function is defined
by the equation
y = f(x) and (a, b) is a
point on the graph, then
the derivative of f at
(a, b) can be thought of in
at least two ways.
• It is the slope of the line
that is tangent to the
curve at (a, b).
• It is the instantaneous rate at which the y-value of the function is
changing as the x-value increases through x = a. We often call this
the derivative at x = a rather than the derivative at (a, b).
In this activity, you will work with this new idea in connection with
some familiar situations. Keep in mind that you can find derivatives by
using smaller and smaller intervals around a particular value of a.
1. The function h(t) = 400 – 16ť gives the height of the supply bundle
(in feet) t seconds after it is dropped from a height of 400 feet.
a. Find the derivative of this function at the point (3, 256).
b. What does your answer tell you about the speed at which the
supply bundle is falling?
2. The function A(t) = ¤(70 + 6t)² gives the area of the oil slick (in
square meters) t hours after Lindsay first spots it.
a. Find the rate at which the area is growing exactly one hour after
Lindsay first saw it.
b. Express your answer as a derivative.

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