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| PAGE: 147 | SET: Exercises | PROBLEM: 69 |
The equation is 
.
(a)
Graph :
Graph for the equation .
(b)
Find the tangent curves at 
.
Find the point of tangency.
Substitute in the equation .
and 
The point of tangents are 
, 
, 
and 
.
The curve equation is .
Apply derivative on each side with respect to 
.
.
The slope at the point 
.
.
Point slope form of line equation : 
.
Substitute 
and in the point slope form.
The tangent line is 
.
The slope at the point 
.
.
Point slope form of line equation : .
Substitute 
and in the point slope form.
The tangent line is 
.
The slope at the point 
.
.
Point slope form of line equation : .
Substitute 
and in the point slope form.
The tangent line is 
.
The slope at the point 
.
.
Point slope form of line equation : .
Substitute 
and in the point slope form.
The tangent line is 
.
(b).
Graph :
Graph the curve equation .
Graph the tangent lines , 
, 
and .
.gif)
(a)
Graph of the curve equation :
(b) The tangent points are , , and .
(c)
Graph of the curve equation :
Graph of the tangent lines , , and :
.
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