Concept explainers
a.
To sketch: the solution curve that passes through the point (0, 1) and sketch the solution curve that goes through the point (0, -1).
a.
Answer to Problem 4QQ
Explanation of Solution
Given information: Consider the differential equation
Calculation:
Draw the solution curve passing through (0, 1) (shown in red) and (0, -1) (shown in green) using the slope of the line segments in the slope field to approximate the slope of the curves at different values of x .
b.
To find: the value of b for which
b.
Answer to Problem 4QQ
Explanation of Solution
Given information:
Calculation:
The slope of
c.
To prove: analytically that g has a
c.
Answer to Problem 4QQ
(0, 0) is a local maximum.
Explanation of Solution
Given information: Let g be the function that satisfies the given differential equation
with the initial condition g (0) = 0.
Calculation:
By second derivative lest, any critical point, in this case (0, 0) is a local maximum.
Chapter 7 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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