(a)
To show: The given function satisfies the mean value theorem within given interval.
(a)
Answer to Problem 37RE
The given function satisfies mean value theorem.
Explanation of Solution
Given:
The function is
Calculation:
According to the Mean value theorem, if any function is continuous on any closed interval
Hence, he given function f(x) is continuous on
Conclusion:
The given function satisfies mean value theorem.
(b)
The value of c in (a,b).
(b)
Answer to Problem 37RE
The value of c is
Explanation of Solution
Given:
The function is
Calculation:
Now, use the value of a and b to solve:
Conclusion:
The value of c is
(c)
The equation for the secant line AB.
(c)
Answer to Problem 37RE
The equation for secant line is
Explanation of Solution
Given:
The function is
Calculation:
The slope of a line is:
Now, the line passes through
Hence, the equation becomes:
Conclusion:
The equation for secant line is
(d)
The equation for the tangent line which is parallel to secant line AB.
(d)
Answer to Problem 37RE
The equation for tangent line is
Explanation of Solution
Given:
The function is
Calculation:
The slope of a line is:
Now, the line passes through:
Conclusion:
The equation for tangent line is
Chapter 4 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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