Concept explainers
a.
To show that
a.
Explanation of Solution
Given:
The function is
Calculation:
According to mean value theorem
Below is the graph of
From graph of
Therefore,
b.
To find the values of
b.
Answer to Problem 37RE
The value of
Explanation of Solution
Given:
The function is
Calculation:
According to mean value theorem
Since, from part (a) it is proved that
Here
So ,
Since,
Therefore, the value of
c.
To write an equation for the secant line
c.
Answer to Problem 37RE
The equation of secant is
Explanation of Solution
Given:
The function is
Calculation:
,
Therefore,
Equation of secant given two points
Therefore, the equation of secant is
d.
To write an equation for the tangent line that is parallel to the secant line
d.
Answer to Problem 37RE
The equation of tangent is
Explanation of Solution
Given:
The function is
Calculation:
Since, it is given that tangent line is parallel to the secant line
General equation of line with slope
Equation of secant line is
On comparing equation of secant line with general equation of line
Slope
Equation of tangent is
Therefore, the equation of tangent is
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic
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