3. Where is f(x) = concave up? Justify your answver. %3D

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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3. Where is f(x) =
concave up? Justify your answver.
4. On what x interval(s) is f(x) = (x- 2) increasing? Justify your answer.
5. In the right-triangle shown, the angle e is increasing at a constant rate of 2
radians per hour. At what rate is the side length of x increasing when x= 4
A?
6. The diameter and height of a paper cup in the shape of a cone are both 4 inches. Water is
leaking out at the rate of țin /sec . Find the rate at which the water level is dropping when the
diameter of the surface is 2 inches.
7. Where is the derivative of f(x) =x' – 3x + 6x increasing? Justify your answer.
Transcribed Image Text:3. Where is f(x) = concave up? Justify your answver. 4. On what x interval(s) is f(x) = (x- 2) increasing? Justify your answer. 5. In the right-triangle shown, the angle e is increasing at a constant rate of 2 radians per hour. At what rate is the side length of x increasing when x= 4 A? 6. The diameter and height of a paper cup in the shape of a cone are both 4 inches. Water is leaking out at the rate of țin /sec . Find the rate at which the water level is dropping when the diameter of the surface is 2 inches. 7. Where is the derivative of f(x) =x' – 3x + 6x increasing? Justify your answer.
1. Consider the curve given by 3y – 12y = 2x +36
a) Find /dx
b) Find the coordinates of all points on the curve at which the line tangent to the curve is
vertical.
c) Find the coordinates of all points on the curve at which the line tangent to the curve is
horizontal.
d) Find in tems of x and y. Are the coordinates found in part c) relative minimums,
maximums or neither? Justify your responses.
2. Find the x-coordinates of the points of inflection of the graph of y =x - 5x* + 3x+7.
Transcribed Image Text:1. Consider the curve given by 3y – 12y = 2x +36 a) Find /dx b) Find the coordinates of all points on the curve at which the line tangent to the curve is vertical. c) Find the coordinates of all points on the curve at which the line tangent to the curve is horizontal. d) Find in tems of x and y. Are the coordinates found in part c) relative minimums, maximums or neither? Justify your responses. 2. Find the x-coordinates of the points of inflection of the graph of y =x - 5x* + 3x+7.
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