- #1
mathmari
Gold Member
MHB
- 5,049
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Hey!
I am looking at the following:
The differentiable and so also continuous function gets its global maximum at a point . Show that the following holds
Could you give me a hint what we are supposed to do? (Wondering)
I have done the following:
Since the function has its global maximum at we have that .
We use the definition of the derivative at :
For we have the following:
Let . We have the interval . , and so is well defined for .
Then we have:
For we have the following:
Let . We have the interval . , and so is well defined for . So, it holds that .
Then we have:
For we have the following:
Is everything correct? Could I improve something? Are the one-sided limits correct? (Wondering)
I am looking at the following:
The differentiable and so also continuous function
Could you give me a hint what we are supposed to do? (Wondering)
I have done the following:
Since the function has its global maximum at
We use the definition of the derivative at
For
Let
Then we have:
For
Let
Then we have:
For
Is everything correct? Could I improve something? Are the one-sided limits correct? (Wondering)