Course:MATH102/Question Challenge/2008 December Q2a
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Question
The following problems require little or no computation. Put the answer in the box provided. You may use space here for supporting reasoning or computations, if any, for which part-marks would be awarded.
Suppose is a function having the following properties: . Suppose is the inverse function for . Then the slope of the tangent line to at the point is:
Hints
Hint |
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At corresponding points, the slopes of inverse functions are related.. how? |
Solutions
Solution |
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Given: , we know that the point is on the graph of the function , and hence the point is on the graph of the function , i.e. . We also use the fact that at these corresponding points, the slopes of the tangent lines to the function and its inverse are reciprocals. Hence, since , we conclude that . For a summary of such properties of inverse functions, see slides 55-59 in [1] |