To find : the two points where the curve crosses the x − axis and show that tangents at these points are parallel.
Answer to Problem 49E
The intersections of curve on x − axis is
The common slope is
Explanation of Solution
Given information :
The curve is
Formula needed :
Chain rule of derivative:
Product rule of derivative:
Tangent line to curve is
When the curve intersects the x − axis,
Substitute
Take square root on both sides,
The intersections of curve on x − axis is
For slope, differentiate
Solve further,
Plug point
The tangent line to point
Hence,
Plug point
The tangent line to point
Hence,
Since, the slope of both tangent line is same. So, the lines are parallel to each other.
Hence, the common slope is
Chapter 3 Solutions
CALCULUS-W/XL ACCESS
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