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| PAGE: 175 | SET: Exercises | PROBLEM: 36 |
(a)
The function is 
.
Find the secant line passing through the points 
and 
.
The equation of a secant line passing through two points is 
The equation of secant line is 
.
(b)
Mean value Theorem :
If 
is continuous on 
and differentiable on open interval 
, then there exists a number 
in such that 
.
The function 
is continuous on the interval 
and differentiable on the interval 
.
So there exists a number in 
such that 
.
The function is .
Apply derivative on each side with respect to 
.
The value of 
in the interval is 
.
(c)
Find the equation of tangent line passing through 
and whose slope is parallel to slope of the secant line.
The secant line equation is 
.
Compare the above equation with the slope intercept form 
.
The slope of the secant line is 
.
Point slope form of the equation is 
.
Therefore the equation of tangent line is 
.
(d)
Graph the function and tangent line 
.
(a) The equation of secant line is .
(b) The value of in the interval is 
.
(c) The equation of tangent line is .
(d)
.
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