- #1
tomboi03
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a. Suppose f is twice differentiable on (0, infinity). Suppose that |f(x)|< or equal A0 for all x>0 and that the second derivative satisfies |f''(x)|< or equal A2 for all x>0.
Prove that for all x>0 and all h>0
|f'(x)| < or equal 2A0/h + A2h/2
This is sometimes called Landau's inequality.
b. Use part a to show that for all x>0
|f'(x)| < or equal 2 sqrt(A0A2)
I have no idea how to go about this problem.
Should I just try to do this problem backwards by trying to find what f(x) by using the f'(x)?
Thanks
Prove that for all x>0 and all h>0
|f'(x)| < or equal 2A0/h + A2h/2
This is sometimes called Landau's inequality.
b. Use part a to show that for all x>0
|f'(x)| < or equal 2 sqrt(A0A2)
I have no idea how to go about this problem.
Should I just try to do this problem backwards by trying to find what f(x) by using the f'(x)?
Thanks