Course:MATH102/Question Challenge/2002 December Q6
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{{#w4grb_rate:}} Hard Easy |
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Question
Consider the curve
This curve intersects the line at a point in the first quadrant . Find the slope of the tangent line to the curve at . Show that this tangent line is perpendicular to the line .
Hints
Hint |
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Consider implicit differentiation, and don't forget to use the product rule on the term . |
Solution
Solution |
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This is a problem in which implicit differentiation is to be used. The equation is
To solve for we derive each term with respect to and solve isolate for , remembering to use the chair rule and product rules where needed.
We know that the curve intersects the line , so we can substitute for :
The slope of the line is equal to . By proving the curve has a slope of at the intersection point, we have shown that the tangent line of the curve at the intersection point is perpendicular to the tangent of the line . |