Suppose f: IR→IR is a moNotonically increasing funckian, = 0 , then fioo = 0 6) Give an example of a funetion 9 and a point xe IR such that but glx) does not exist (a) Prave Lim fixh) - fix-h) Lim 9x+h] -g\<
Suppose f: IR→IR is a moNotonically increasing funckian, = 0 , then fioo = 0 6) Give an example of a funetion 9 and a point xe IR such that but glx) does not exist (a) Prave Lim fixh) - fix-h) Lim 9x+h] -g\<
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter8: Linear Functions
Section8.7: Function Notation
Problem 2E
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Step 1
Answer for sub question a:
Suppose is a monotonically increasing function and suppose
Then since is monotonically increasing it is differentiable almost everywhere and since it follows that is differentiable at .
Now, since is differentiable at ,
Now,
Hence,
Therefore,
Hence the claim.
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